https://www.causeweb.org/wiki/chance/api.php?action=feedcontributions&user=Nano12&feedformat=atomChanceWiki - User contributions [en]2024-03-28T23:10:15ZUser contributionsMediaWiki 1.40.0-alphahttps://www.causeweb.org/wiki/chance/index.php?title=ChanceWiki:General_disclaimer&diff=1576ChanceWiki:General disclaimer2005-11-05T09:35:44Z<p>Nano12: </p>
<hr />
<div><br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div></div>Nano12https://www.causeweb.org/wiki/chance/index.php?title=Chance_News_7&diff=1567Chance News 72005-11-05T09:35:38Z<p>Nano12: /* Further reading */</p>
<hr />
<div>Sept 26 2005 to Oct 15 2005<br />
==Quotation==<br />
<blockquote><br />
While writing my book [Stochastic Processes] I had an argument with Feller [Introuction to Probability Theory and its Applications]. He asserted that everyone said "random variable" and I asserted that everyone said "chance variable." We obviously had to use the same name in our books, so we decided the issue by a stochastic procedure. That is, we tossed for it and he won. </blockquote><br />
<br />
<p align = right> Joe Doob<br><br />
[http://www.dartmouth.edu/~chance/Doob/conversation.html Statistical Science]<br><br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Forsooth==<br />
<br />
Peter Winkler suggested our first forsooth.<br />
<br />
<blockquote>Texas beats Ohio State in their opening game <br />
of the season (Saturday Sept 10 2002). The sportscasters (legendary Brent Musburger on play-by-play or Gary Danielson on analysis) observed that of the 14 teams who have <br />
previously played in the championship game (at the end of each season) 5 <br />
have suffered an earlier defeat. "Thus," they conclude, "Ohio State can <br />
still make it to the championship game, but their chances are now less <br />
than 50%."</blockquote><br />
<br />
===Discussion===<br />
<br />
What is wrong with this?<br />
----<br />
Here are forsooths from the September 2005 issues of RSS NEWS<br />
<br />
<blockquote>'Big ticket quiz' at the start of Wimbledon:<br><br><br />
Q. How many punnets (a small light basket or other container for fruit or vegetables) of strawberries are eaten each day during the Wimbledon tournament?<br><br />
Is it (a) over 8,000, (b) over 9,000 or (c) over 10,000?</blockquote><br />
<br />
<div align="right">BBC radio 5<br><br />
20 June 2005</div><br />
<br />
<blockquote>Waiting time for foot surgery down by 500%</blockquote><br />
<br />
<div align="right">Evening News (Edinburgh)<br><br />
5 July 2005</div><br />
<br />
The next two forsooths are from the October RSS news.<br />
<br />
<blockquote>In 1996-8 when the number attending university was static, the participation of women was also static, but male participation fell.</blockquote><br />
<br />
<div align="right">The Times Higher<br><br />
21 January 2005</div><br />
<br />
<blockquote>[On the subject of congestion on the London Underground..] 'Last year 976 million of us used the tube...'</blockquote><br />
<br />
<div align="right">BBC London News<br><br />
19 May 2005</div><br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Fortune's Formula==<br />
<br />
''Fortune's Formula: Wanna Bet?''<br><br />
''New York Times Book Section'', September 25, 2005<br><br />
David Pogue<br />
<br />
This must be the kind of review that every Science writer dreams of. Pogue ends his review with:<br />
<br />
<blockquote> ''Fortune's Formula'' may be the world's first history book, gambling primer, mathematics text, economics manual, personal finance guide and joke book in a single volume. Poundstone comes across like the best college professor you ever had, someone who can turn almost any technical topic into an entertaining and zesty lecture. But every now and then, you can't help wishing there were some teaching assistants on hand to help.</blockquote><br />
<br />
The author William Poundstone is a science writer who has written a number of very successful science books. His book, ''Prisoner's dilemma: John von Neumann, game theory and the puzzle of the bomb'', was written in the style of this book. Indeed Helen Joyce, in her review of this book in Plus Magazine writes:<br />
<br />
<blockquote>This book is a curious mixture of biography, history and mathematics, all neatly packaged into an entertaining and enlightening read. </blockquote><br />
<br />
Poundstone describes himself as a visual artist who does books as a "day job.". You can learn about his art work [http://www.uiowa.edu/~iareview/tirweb/feature/poundstone/interview2.htm here].<br />
<br />
''Fortune's Formula'' is primarily the story of Edward Thorp, Claude Shannon, and John Kelly and their attempt to use mathematics to make money gambling in casinos and on the stock market. None of these did their graduate work in mathematics. Thorp and Kelly got their Phd's in physics and Shannon in Genetics. <br />
<br />
In the spring of 1955, while a graduate student at UCLA, Thorp joined a discussion on the possiblity of making money from roulette. Thorp suggested that they could taking advantage of the fact that bets are still accepted for a few second after the croupier releases the ball, and in these seconds, he could estimate what part of the wheel the ball would stop. <br />
<br />
Thorp did not pursue this and in 1959 became an instructor in mathematics at M.I.T. Here he became interested in blackjack and developed his famous card counting method for wining at blackjack. He decided to publish his method in the most prestigious journal he could find and settled on ''Proceedings of the National Academy of Sciences''. For this he needed to have a member of the Academy submit his paper. The only member in the math department was Shannon so he had to persuade him of the importance of his paper. Shannon not only agreed but in the process became fascinated by Thorp's idea for beating roulette. He agreed to help Thorp carry this out. They built a roulette machine in Shannon's basement. It worked fine there in trial runs but not so well in the casino so they did not pursue this method of getting rich. <br />
<br />
Of course Thorp is best known for showing that blackjack is a favorable game and giving a method to exploit this fact. Shannon is best known for his work in information theory. Kelly is known his method for gambling in a favorable game. This plays a central role in Poundstone's book and is probably why Pogue felt that it would help if he had a teaching assistant. Poundstone tries to explain Kelly's work in many different ways but what he really needed to understand it is an example but this required too many formulas for a popular book. So we shall include an example from Chance News 7.09. <br />
<br />
Writing for Motley Fool, 3 April 1997 Mark Brady complained about the inumeracy of the general public and gave a number of examples including this one:<br />
<br />
<blockquote> Fear of uncertainty and innumeracy are synergistic. Most people cannot do the odds. What is a better deal over a year? A 100% safe return with 5 percent interest or a 90 percent safe return with a 20 percent return. For the first deal, your return will be 5% percent. For the second, your return will be 8%. Say you invest $1000 10 times. Your interest for the 9 successful deals will be 9000 x 0.2 or 1800. Subtract the 1000 you lost on the 10th deal and you get a $800 return on your original $10,000 for 8 percent.</blockquote><br />
<br />
Peter Doyle suggested that a better investment strategy in this case is:<br />
<br />
Faced with a 100 percent-safe investment returning 5 percent and a 90 percent-safe investment returning 20%, you should invest 20% of your funds in the risky investment and 80% in the safe investment. This gives you an effective return of roughly 5.31962607969968292 percent. <br />
<br />
Peter is using a money management system due to J. L. Kelly (1956: "A new interpretation of information rate," ''Bell System Technical Journal'', '''35'''). Kelly was interested in finding a rational way to invest your money faced with one or more investment schemes, each of which has a positive expected gain. He did not think it reasonable to try simply to maximize your expected return. If you did this in the Motley Fools example as suggested by Mark Brady, you would choose the risky investment and might well lose all your money the first year. We will illustrate what Kelly did propose in terms of Motley Fools example. <br />
<br />
We start with an initial capital, which we choose for convenience to be $1, and invest a fraction r of this money in the gamble and a fraction 1-r in the sure-thing. Then for the next year we use the same fractions to invest the money that resulted from the first year's investments and continue, using the same r each year. Assume, for example, that in the first and third years we win the gamble and in the second year we lose it. Then after 3 years our investment returns an amount f(r) where: <br />
<br />
<math><br />
f(r) = (1.2r + 1.05(1-r))(1.05(1-r))(1.2r + 1.05(1-r)). <br />
</math><br />
<br />
After n years, we would have n such factors, each corresponding to a win or a loss of our risky investment. Since the order of the terms does not matter our capital will be: <br />
<br />
<math><br />
f(r,n) = (1.2r + 1.05(1-r))^W(1.05(1-r))^L<br />
</math><br />
<br />
where W is the number of times we won the risky investment and L the number of times we lost it. Now Kelly calls the quantity:<br />
<br />
<math><br />
G(r) =\lim_{n \to \infty }\frac{\log(f( r,n)} {n}<br />
</math> <br />
<br />
the exponential rate of growth of our capital. In terms of G(r) our capital should grow like <math> e^{G(r)} </math>. In our example: <br />
<br />
<math><br />
\log(\frac{f(r,n)}{n}) = \frac{W}{n}\log(1.2r + 1.05(1-r)) + \frac{L}{n}\log(1.05(1-r))<br />
</math> <br />
<br />
Since we have a 90% chance of winning our gamble, the [http://en.wikipedia.org/wiki/Strong_law_of_large_numbers#The_strong_law strong law of large numbers] tells us that as n tends to infinity this will converge to <br />
<br />
<math><br />
G(r) = 0.9\log(1.2r + 1.05(1-r))+0.1\log(1.05(1-r))<br />
</math><br />
<br />
It is a simple calculus problem to show that G(r) is maximized by r = 0.2 with: <br />
G(0.2) = 0.05183. Then e^{0.05183} = 1.0532, showing that our maximum rate of growth is 5.32% as claimed by Peter. <br />
<br />
The attractiveness of the Kelly investment scheme is that, in the long run, any other investment strategy (including those where you are allowed to change your investment proportions at different times) will do less well. "In the long run and less well" means more precisely that the ratio of your return under the Kelly scheme and your return under any other strategy will tend to infinity.<br />
<br />
Thorp had a very good experience in the stock market, which is described very well by Gaeton Lion in his excellent [http://www.amazon.com/gp/product/customer-reviews/0809046377/ref=cm_cr_dp_pt/103-8647004-5865443?%5Fencoding=UTF8&n=283155&s=books review] of ''Fortune's Formula''. He writes:<br />
<br />
<blockquote> Ed Thorp succeeded in deriving superior returns in both gambling and investing. But, it was not so much because of Kelly's formula. He developed other tools to achieve superior returns. In gambling, Ed Thorp succeeded at Black Jack by developing the card counting method. He just used intuitively Kelly's formula to increase his bets whenever the odds were in his favor. Later, he ran a hedge fund for 20 years until the late 80s and earned a rate of return of 14% handily beating the market's 8% during the period. <br><br><br />
<br />
Also, his hedge fund hardly lost any value on black Monday in October 1987, when the market crashed by 22%. The volatility of his returns was far lower than the market. He did this by exploiting market inefficiencies using warrants, options, and convertible bonds. The Kelly formula was for him a risk management discipline and not a direct source of excess return. </blockquote><br />
<br />
Shannon also made a lot of money on the stock market, but did not use Kelly's formula. In his [http://www.amazon.com/gp/product/customer-reviews/0809046377/ref=cm_cr_dp_pt/103-8647004-5865443?%5Fencoding=UTF8&n=283155&s=books review] Gaeton Lion writes<br />
<br />
<blockquote>Claude Shannon amassed large wealth by recording one of the best investment records. His performance had little to do with Kelly's formula. Between 1966 and 1986, his record beat even Warren Buffet (28% to 27% respectively). Shannon strategy was similar to Buffet. Both their stock portfolios were concentrated, and held for the long term. Shannon achieved his record by holding mainly three stocks (Teledyne, Motorola, and HP). The difference between the two was that Shannon invested in technology because he understood it well, while Buffet did not. </blockquote><br />
<br />
Finally, Thorp provided the following comments for the book cover:<br />
<br />
<blockquote>From bookies to billionaires, you'll meet a motley cast of characters in this highly original, 'outside the box' look at gambling and investing. Read it for the stories alone, and you'll be surprised at how much else you can learn without even trying. --Edward O. Thorp, author of ''Beat the Dealer'' and ''Beat the Market''.</blockquote><br />
<br />
Submitted by Laurie Snell.<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Which foods prevent cancer?==<br />
<br />
Which of these foods will stop cancer? (Not so fast)<br><br />
New York Times, 27 September 2005, Sect. F, p. 1<Br><br />
Gina Kolata<br />
<br />
Among other examples, the article includes a [http://www.nytimes.com/imagepages/2005/09/26/science/20050927_CANCER_GRAPHIC.html data graphic] on purported benefits of dietary fiber in preventing colorectal cancer. Early observational studies indicated an association, but subsequent randomized experiments found no effect. <br />
<br />
More to follow.<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Slices of risk and the <em>broken heart</em> concept==<br />
[http://www.gloriamundi.org/picsresources/news20050912.pdf How a Formula Ignited Market That Burned Some Big Investors],<br />
Mark Whitehouse, The Wall Street Journal, September 12, 2005.<br><br />
<br />
This on-line article relates how a statistician, David Li,<br />
unknown outside a small coterie of finance theorists, helped change the world of investing. <br />
<br />
The article focuses on a event last May when General Motors Corp's debt<br />
was downgraded to junk status, causing turmoil in some financial markets.<br />
The article gives a nice summary of the underlying financial instruments known<br />
as credit derivatives -<br />
investment contracts structured so their value depends on the behavior of some other thing or event -<br />
with exotic names like <br />
[http://en.wikipedia.org/wiki/Collateralized_debt_obligations collateralized debt obligations] and [http://en.wikipedia.org/wiki/Credit_default_swap credit-default swaps].<br />
<br />
The critical step is to estimate the likelihood that many of the companies <br />
in a pool of companies would go bust at once. <br />
For instance, if the companies were all in closely related industries,<br />
such as auto-parts suppliers, they might fall like dominoes after a catastrophic event.<br />
Such a pool would have a 'high default correlation'.<br />
<br />
In 1997, nobody knew how to calculate default correlations with any precision. <br />
Mr. Li's solution drew inspiration from a concept in actuarial science known as the <br />
<em>broken heart</em> syndrome - people tend to die faster after the death of a beloved spouse. <br />
Some of his colleagues from academia were working on a way to predict this<br />
death correlation, something quite useful to companies that sell life insurance and joint annuities.<br />
He says:<br />
<blockquote><br />
Suddenly I thought that the problem I was trying to solve was exactly like the problem these<br />
guys were trying to solve,.<br />
Default is like the death of a company, so we should<br />
model this the same way we model human life."<br />
</blockquote><br />
<br />
This gave him the idea of using [http://en.wikipedia.org/wiki/Copula_%28statistics%29 copulas], <br />
mathematical functions the colleagues had begun applying to actuarial science. <br />
Copulas help predict the likelihood of various events<br />
occurring when those events depend to some extent on one another. <br />
Until the events last May of this year, one of the most popular copulas for bond pools <br />
was the Gaussian copula, named after <br />
[http://en.wikipedia.org/wiki/Carl_Friedrich_Gauss Carl Friedrich Gauss], a 19th-century German statistician. <br />
<br />
===Further reading===<br />
* The [http://www.gloriamundi.org/picsresources/news20050912.pdf on-line article] gives more details about what went wrong in the financial markets in May and the search for a more appropriate copula to capture better the <em>broken heart</em> syndrome between companies.<br />
* [http://en.wikipedia.org/wiki/Wikipedia Wikipedia] is a very worthwhile on-line resource for definitions of technical words, such as [http://en.wikipedia.org/wiki/Copula_%28statistics%29 copula].<br />
<br />
Submitted by John Gavin.<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Learning to speak via statistics and graph theory==<br />
<br />
[http://education.guardian.co.uk/tefl/teaching/story/0,15085,1576100,00.html Computer learns grammar by crunching sentences], Max de Lotbinière September 23, 2005, [http://www.guardianweekly.co.uk/ Guardian Weekly].<br><br />
[http://www.cornellsun.com/vnews/display.v/ART/2005/09/09/432118a84f6af Profs’ New Software ‘Learns’ Languages], Ben Birnbaum, 9 Sep 2005, Cornell Daily Sun.<br />
<br />
A language-learning robot may sound like science fiction but new software, developed by Cornell University psychology professor Shimon Edelman, with colleagues Zach Solan, David Horn and Eytan Ruppin from Tel Aviv University in Israel, is well on the way to constructing a computer program that can teach itself languages and make up its own sentences, the developers' claim.<br />
<br />
Unlike previous attempts at developing computer algorithms for language learning - "Automatic Distillation of Structure," or "ADIOS" for short - discovers complex patterns in raw text by repeatedly aligning sentences and looking for overlapping parts.<br />
Once it has derived a language's rules of grammar,<br />
it can then produce sentences of its own, simply from blocks of text in that language.<br />
<br />
It has been evaluated on artificial context-free grammars with thousands of rules, <br />
on natural languages as diverse as English and Chinese, <br />
on coding regions in DNA sequences and on protein data correlating sequence with function. <br />
<br />
Edelman comments:<br />
<blockquote><br />
Adios relies on a statistical method for pattern extraction and on structured generalisations <br />
- the two processes that have been implicated in language acquisition.<br />
Our experiments show that Adios can acquire intricate structures <br />
from raw data including transcripts of parents' speech directed at two- or three-year-olds.<br />
This may eventually help researchers understand how children, <br />
who learn language in a similar item-by-item fashion, and with little supervision, <br />
eventually master the full complexity of their native tongue.<br />
</blockquote><br />
<br />
[http://plus.maths.org/latestnews/may-aug05/adios/ Plus Magazine's website]<br />
offers a more logical explanation:<br />
<blockquote><br />
The ADIOS algorithm is based on statistical and algebraic methods performed on one of the most basic and versatile objects of mathematics - the graph.<br />
Given a text, the program loads it as a graph by representing each word by a node, or vertex, and each sentence by a sequence of nodes connected by lines. A string of words in the text is now represented by a path in the graph. <br><br />
<br />
Next it performs a statistical analysis to see which paths, or strings of words, occur unusually often. <br />
It then decides that those that appear most frequently - called "significant patterns" - <br />
can safely be regarded as a single unit<br />
and replaces the set of vertices in each of these patterns by a single vertex, <br />
thus creating a new, generalised, graph.<br><br />
<br />
Finally, the program looks for paths in the graph which just differ by one vertex. <br />
These stand for parts of sentences that just differ by one word (or compound of words) like "the cat is hungry" and "the dog is hungry". <br />
Performing another statistical test on the frequency of these paths, the program identifies classes of vertices, or words, that can be regarded as interchangeable, or equivalent. <br />
The sentence involved is legitimate no matter which of the words in the class - in our example "cat" or "dog" - you put in.<br><br />
<br />
This last step is then repeated recursively.<br><br />
</blockquote><br />
<br />
[http://plus.maths.org/latestnews/may-aug05/adios/ The website] uses graphs to illustrate some examples and it finishes with some reassuring words:<br />
<blockquote><br />
All this doesn't mean, of course, that the program actually "understands" what it's saying. It simply knows how to have a good go at piecing together fragments of sentences it has identified, in the hope that they are grammatically correct. So if, like me, you're prone to swearing at your computer, you can safely continue to do so: it won't answer back for a long while yet.<br />
</blockquote><br />
<br />
===Further reading===<br />
The [http://adios.tau.ac.il/ ADIOS homepage] offers an overview and more detailed description of the program.<br />
<br />
Submitted by John Gavin.<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Understanding probability==<br />
<br />
Understanding Probability:Chance rules in everyday life<br><br />
Cambridge University Press 2004<br><br />
Henk Tijms<br />
<br />
Hank Tijms is Professor in Operation Research at the Vrije University in Amsterdam. This book is based on his earlier Dutch book “Spelen met Kansen.” <br />
<br />
The aim of this book is to show how probability applies to our everyday life in a way that your Uncle George could understand even if he has forgotten much of his high school math. Tijms does not try to avoid mathematics but only to postpone the formal math until the reader has seen the many applications of probability in the real world, how much fun it is, and learned to work problems and when he can’t work one how to get the answer by simulation. He learns all this in part I of the book and then he learns the more formal math in Part II.<br />
<br />
In Chapter 1 Tijms asks the reader to think about problems with surprising answers in the spirit of Susan Holmes “[http://www-stat.stanford.edu/~susan/surprise/ Probability by Surprise]” including the birthday problem and the Monty Hall problem. Readers are on their own to try to solve one or more of the problems but promised that they will see the solutions later in the book. <br />
<br />
Chapter 2 deals with the law of large numbers and introduces the concept of simulation. This theorem is explained and illustrated by problems related, for example, to coin tossing, random walks and casino games. Expected value is introduced in an informal way to be defined more carefully later in the book. For the reader who is not frightened by mathematical formulas, Tijms includes a discussion of the Kelly betting system with a footnote saying that this paragraph can be skipped at first reading. This is a fascinating topic that is widely applied in gambling and stock investment but rarely appears in a probability book.<br />
<br />
In Chapter 3 the author returns to previous problems such as the birthday problem and gambling systems and solves them first by simulation and then by mathematics. <br />
<br />
In this chapter Tijms describes Efron’s bootstrap method and uses it to solve a number of problems including a hypothetical clinical trial and to test if the famous 1970 draft lottery during the Vietnam War was fair. Again the bootstrap method has wide application but rarely occurs in an elementary probability or statistics book.<br />
<br />
Chapter 4 describes the binomial, Poisson, and hypergeomtric distributions and how to use them in solving problems such as the famous hat check problem, and a variety of interesting lottery questions. The Poisson process is discussed but again with the footnote that novice readers might want to read this at a later time.<br />
<br />
Chapter 5 is mainly about Center Limit Theorem and its many applications especially to statistics. <br />
<br />
Chapter 6 introduces Chance trees and Bayes’s rule. The tree method is used to explain a variety of problems including the Monty Hall Problem and the false-positive paradox. <br />
<br />
This is a brief description of the first six chapters which constitute Part I of the book. Now the fun is over. Part 2 called “Essentials of probability” looks like the traditional first chapters in a standard probability book. But the reader has already found how exciting probability is, has a good intuitive idea of the basic concepts and has worked many of the interesting problems at the end of each chapter either using math or simulation. For some students this might allow them to actually enjoy Part 2. But your Uncle George may want to quit while they are ahead. <br />
<br />
Tijms writes with great clarity and his enthusiasm for probability in the real world is contagious. We were delighted to see, as acknowledged in the preface, that Tijms included several of the more interesting problems discussed in Chance News, often going well beyond what we had said in our discussion of the problem. <br />
<br />
This book presents a completely new way to go about teaching a first course in probability and we think those who teach such a course should consider trying it out.<br />
<br />
===Discussion===<br />
<br />
(1) In the days of Basic we required all students to learn Basic in their first math course so we could assume that students could write programs to simulate probability problems and so me made heavy use of simulation as suggested in this book. The author uses Pascal in his book. What present language do you think is easiest for a student with no computing experience to learn?<br />
<br />
We asked Professor Tijms what the situation was in math departments in Europe and he replied:<br />
<br />
<blockquote>In math departments of universities and polytechnic schools in Europe students learn to write computer programs. In my university they still learn to program in Java and C++ ( in previous days Pascal), but I see in the Netherlands the trend that the instructors think it is sufficient if the students are able to program in Matlab. <br><br><br />
<br />
In ny book I have chosen to formulate the simulation programs in Pascal because of the clarity and the simplicity of the language, though this language is hardly used anymore. The introductory probability course at my university is given before they have learned to program, but this does not prevent them of simulating probability problems by using Excel. In the simulation of many elementary probability problems a random-number generator alone suffices to simulate those problems and so Excel can be used. In the second year they have mastered Matlab, a perfect tool with its excellent graphics to simulate many challenging probability problems ( they really like it, in particular when it concerns problems such as the problems 2.24-2.45 in chapter 2 and the problems 5.11-5.13 in chapter 5). <br />
</blockquote><br />
<br />
<br />
(2) Do you think that probability books should include data to test probability models that are said to describe real world problems? If so name some models that you think would pass such a test and some that you think might not.<br />
<br />
Submitted by Laurie Snell<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Societies worse off when they have God on their side==<br />
<br />
[http://www.timesonline.co.uk/article/0,,2-1798944,00.html Societies worse off when they have God on their side]<br><br />
Timesonline, September 27, 2005<br><br />
Ruth Gledhill<br />
<br />
[http://moses.creighton.edu/JRS/2005/2005-11.html Cross-national correlations of quantifiable societal health with popular religiosity and secularism in the prosperous democracies]<br><br />
Journal of Religion & Society, Vol.7(2005)<br><br />
Gregory S. Paul<br />
<br />
In the Times article we read:<br />
<br />
<blockquote>According to the study, belief in and worship of God are not only unnecessary for a healthy society but may actually contribute to social problems.<br><br><br />
Many liberal Christians and believers of other faiths hold that religious belief is socially beneficial, believing that it helps to lower rates of violent crime, murder, suicide, sexual promiscuity and abortion. The benefits of religious belief to a society have been described as its “spiritual capital”. But the study claims that the devotion of many in the US may actually contribute to its ills. <br />
</blockquote><br />
<br />
Gregory Paul is a dinosaur paleontologist and on an [http://www.abc.net.au/worldtoday/indexes/2005/twt_20050928.htm interview] on Australian ABC radio Paul said that, being a paleontologist, for many years he had to deal with the issue of creationism versus evolutionary science in the U.S and his interest in evolutionary science prompted him to look at whether there was any link between the religiosity of a society and how well that society functions. <br />
<br />
If you look at Paul's article you will find very little technical statistical analysis, for example, he did not carry out a regression analysis. Rather he rests his case on the series of scatterplots.<br />
<br />
Paul describes his data sources as:<br />
<br />
<blockquote>Data sources for rates of religious belief and practice as well as acceptance of evolution are the 1993 Environment I (Bishop) and 1998 Religion II polls conducted by the International Social Survey Program (ISSP), a cross-national collaboration on social science surveys using standard methodologies that currently involves 38 nations. The last survey interviewed approximately 23,000 people in almost all (17) of the developed democracies; Portugal is also plotted as an example of a second world European democracy. Results for western and eastern Germany are combined following the regions' populations. England is generally Great Britain excluding Northern Ireland; Holland is all of the Netherlands. The results largely agree with national surveys on the same subjects; for example, both ISSP and Gallup indicate that absolute plus less certain believers in a higher power are about 90% of the U.S. population. The plots include Bible literalism and frequency of prayer and service attendance, as well as absolute belief in a creator, in order to examine religiosity in terms of ardency, conservatism, and activities. </blockquote><br />
<br />
Here are the countries Paul considered with the abbreviations used on the graphics. <br />
<br />
A = Australia, C = Canada, D = Denmark, E = Great Britain, F = France, G = Germany,<br />
H = Holland, I = Ireland, J = Japan, L = Switzerland, N = Norway, P = Portugal, R = Austria,<br />
S = Spain, T = Italy, U = United States, W = Sweden, Z = New Zealand.<br />
<br />
There seems to be no agreement as to which countries are developed democracies. For example Paul might have included Greece and Belgium, Finland, and others but the data may have determined his choice. Paul comments that he added Portugal as an example of a second world democracy. <br />
<br />
Paul's anaysis of the data includes a series of 9 Figures which are available at the end of the article and are the most interesting part of the study. If you try printing Paul's article you will only get the first of his 9 Figures. When you look at the [http://moses.creighton.edu/JRS/2005/2005-11.html web version] you will still see only Figure 1 but the others can be viewed by selecting the numbers from 2 to 9 on the left side of Figure 1.<br />
<br />
Figure 1 deals with the proportion of people who accept human evolution which is interesting but not as relevant to the welfare of the people as others so we will look at Figure 2.<br />
<br />
[[Image:religion2.png|500px|center|Source:Gregory Paul]]<br />
<br />
Each Figure iprovides 5 separate scatterplots. Ïn Figure 2 we see that the U.S. has largest number--between 6 and 7-- of homicides per 100,000 and Spain has the lowest number with less than 1 homicide per 100,000. We also see that the U.S. has the highest proportion of people, about 25%, who take the bible literally while several countries have less than 10% such people.<br />
<br />
What we cannot do is compare the number of homicides per thousand between those who take the bible literally and those who are agnostics or atheists which is what we would really want to know. Presumably the data did not permit this comparison. <br />
<br />
[[Image:religion3.png|500px|center|Source:Gregory Paul]]<br />
<br />
Figure 3 deals with "14-24 year old suicides per 100,000". Here the U.S. is in about the middle.<br />
<br />
Figure 4 deals with the "under-five mortalities per 1000 births".<br />
<br />
[[Image:religion4.png|500px|center|Source:Gregory Paul]]<br />
<br />
Ignoring Portugal, the U.S. has the highest number of under-five mortalities per 1000 births-- between 7 and--8 while several countries have only 4.<br />
<br />
The other figures can be seen at end of Paul's article. They deal with life expectancy, sexually transmitted diseases, abortion and 15-16 year old pregnancies. Life expectancy is the smallest in the U.S. and for sexually transmitted diseases, abortion and 15-17 year old prenacies the U.S. is at the top of the graphs and in fact these look like outliers.<br />
<br />
Well, this study does not by itself justify the Times hedline: "Societies worse off when they have God on their side." Paul himself would not claim this. He writes:<br />
<br />
<blockquote> This study is a first, brief look at an important subject that has been almost entirely neglected by social scientists. The primary intent is to present basic correlations of the elemental data. Some conclusions that can be gleaned from the plots are outlined. This is not an attempt to present a definitive study that establishes cause versus effect between religiosity, secularism and societal health. It is hoped that these original correlations and results will spark future research and debate on the issue.</block<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div></div>Nano12https://www.causeweb.org/wiki/chance/index.php?title=Chance_News_8&diff=1566Chance News 82005-11-05T09:35:33Z<p>Nano12: /* Mammograms Validated as Key in Cancer Fight */</p>
<hr />
<div>Oct 15 to Oct 30<br />
<br />
==Quotation==<br />
<blockquote>One more fagot of these adamantine bandages, is, the new science of Statistics. It is a rule, that the most casual and extraordinary events -- if the basis of population is broad enough -- become matter of fixed calculation. It would not be safe to say when a captain like Bonaparte, a singer like Jenny Lind, or a navigator like Bowditch, would be born in Boston: but, on a population of twenty or two hundred millions, something like accuracy may be had. Ralph Waldo Emerson Fate</blockquote><br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Forsooth==<br />
Here's another Forsooth from the October issue of RSS News.<br />
<blockquote>Your'e more likely to die in a fire in Strathclyde than anywhere else in the country</blockquote><br />
<br />
<div align="right">BBC1 mews bullietin<br><br />
11 May 2005</div><br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==The Poisson distribution and the Supreme Court==<br />
The Poisson distribution and the Supreme Court<br><br />
''Journal of the American Statistical Association'' 31, no. 195 ,(1936), 376-80<br><br />
W. Allen Wallis<br />
<br />
Supreme Court Appointments as a Poisson distribution<br><br />
''American Journal of Political Science'', 26, No.1, February 1982<br><br />
S. Sidney Ulmer<br />
<br />
This is not current news, but since Supreme Court appointments are in the news we felt that these articles might make an interesting class discussion.<br />
<br />
In 1936 statistician Allen Wallis suggested that a Poisson distribution can approximate the number of U.S. Supreme Court appointments in a given year. In his Table 1 Wallis provided the number appointed in each year over the intervals with different numbers of Justices on the Supreme Court: 1790-1806 (6) 1807-1836 (7), and 1837-1932 (9). Actually there were 10 in the years 1963 to 1967 which Wallis called "negligible exceptions."<br />
<br />
[[Image:wallis1.png|500px|center]]<br />
<br />
Wallis then restricts himself to the years 1837-1932 and finds that a Poisson distribution with mean .5 can approximate the number of court appointments in a year. His results are shown in his Figure II:<br />
<br />
[[Image:wallis2.png|500px|center]]<br />
<br />
In his article, Sidney Ulmer updated the data to 1980 and also includes data from the early Supreme Courts with 6 and 7 members. Thus his data covers the years 1790--1980. His Table 1 compares the actual number of appointments in a year with the expected number of appointments assuming a Poisson distribution with mean 5.13.<br />
<br />
[[Image:ulmer1.png|500px|center]]<br />
<br />
In his Table II Ulmer limits the data to the 9 member Supreme Courts: 1837 to 1862 and 1869-1980).<br />
<br />
[[Image:ulmer2.png|500px|center]]<br />
<br />
Testing the goodness of fits, Ulmer argues that the fit with the varying size Supreme Courts is just as good as with fixed size Supreme Courts.<br />
<br />
===DISCUSSION===<br />
<br />
(1) What is the probability that a President will make 2 or more appointments to the Supreme Court during a 4-year term? What is the probability a President makes no appointments during a 4-year term? Has this ever happened?<br />
<br />
(2) Do you agree with Ulmer that there is no reason to limit the data to years with the Supreme Court is the same size?<br />
<br />
(3) Obtain the data needed to update Ulmer's results to today and provide Tables that correspond to Ulmer's Tables 1 and 2. Add your Tables to this Chance News and make your data available to make it easier to update this in future years.<br />
<br />
Contributed by Laurie Snell<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Possible Cancer Cluster in Connecticut==<br />
Pratt Agrees to Increase Funding for Brain Cancer Study <br><br />
''The Associated Press''<br><br />
October 11, 2005<br><br />
Stephen Singer<br><br />
<br />
<br />
In a case that seems eerily familiar to the leukemia cancer cluster made famous by the book and movie, ''A Civil Action'', researchers are trying to determine whether or not a cancer cluster exists among workers at Pratt & Whitney, a company that manufactures jet engines. Over one hundred former or current Pratt & Whitney employees have been identified as having a relatively rare type of fatal brain tumor known as glioblastoma multiforme, which strikes 3 people per 100,000 every year. Many of these workers have been exposed to metals and chemical substances, including TCE (trichloroethylene), which is an engine degreaser. TCE is the same carcinogenic chemical that was dumped in the 1960’s and 1970’s by the chemical company, WR Grace, in Woburn, MA, and that was found to have contaminated the drinking water in two of the town’s wells. <br><br />
<br />
<br />
Prior to the recent announcement that the funding is being increased from $6 million dollars to $12 million dollars, this medical study was already being described as the largest occupational health study ever conducted. It covers 250,000 people who worked at any of the seven Connecticut Pratt & Whitney plants from 1952 to 2001. So far, at least 125 cases of brain cancer have been documented, according to the lawyer who represents dozens of individuals and family members.<br><br />
<br />
<br />
The study falls under the auspices of the Connecticut Department of Public Health. However, due to the overwhelming cost and scope of the study, Pratt & Whitney is funding the project. Since Pratt is paying for the study, they chose the researchers, a team from the University of Pittsburgh. The project began three years ago, and the results are expected to be available between 2007 and 2009.<br><br />
<br />
<br />
In the meantime, this case faces many of the obstacles common in the quest to establish whether or not a cancer cluster exists, such as proving causation, the fact that it can take a long time (sometimes 5-40 years) after exposure for true problems to show up, and finding the people who were exposed & convincing them to participate in the study. Additionally, there are legal difficulties for the families involved, including Connecticut’s statute of limitations laws, the length of time it takes investigators to reach a conclusion, the cost of litigation, and the “deep pockets” of a company like Pratt & Whitney.<br><br />
<br />
<br />
This case study provides a current example of an ongoing investigation into a possible cancer cluster. Will it ultimately be found to be a coincidence cluster or proven to be a true cancer cluster? Does it make sense that the researchers are including in the study everyone who worked at Pratt over a fifty year period, even those who only worked there for a brief time period and those who were not directly exposed to toxic substances (i.e. office workers)? Could the researchers possibly have an unconscious bias in favor of the company that is funding their research? If the company doesn’t fund the research, then who should? Is there some other way to structure such investigations, so that the company involved pays for the study, but is not allowed to choose the researchers and directly fund them?<br><br />
<br />
<br />
'''Further Reading'''<br><br />
<br />
• “Rare Cancer Found in Workers”, ''The New York Times'', March 10, 2002, Jane Gordon<br><br />
• “Scientist: Pratt Commits to Cancer Study”, ''The Hartford Courant'', May 19, 2005<br><br />
• “Participation in Cancer Study at Pratt Lagging”, ''The Hartford Courant'', October 12, 2005, Paul Marks<br><br />
• ''The New Haven Advocate'' has had more than a dozen articles that explain the working conditions at Pratt & Whitney, and also chronicle the history & progression of this case. These articles have been investigated and written primarily by Carole Bass, Associate Editor. A few of the articles are listed below. <br> <br />
-“Worked to Death”, August 2, 2001, Carole Bass & Camille Jackson<br><br />
-“Talking Cure”, October 28, 2004, Dave Goldberg<br><br />
-“Time’s Not on Their Side”, January 20, 2005, Carole Bass<br><br />
-“The Brains Behind the Brain”, October 20, 2005, Carole Bass <br><br />
For the early New Haven Advocate articles (i.e., 2001-2002) on this subject, go to http://old.newhavenadvocate.com/workedtodeath/index.html<br> <br />
For the articles since 2002, go to <br><br />
http://www.newhavenadvocate.com and search for Pratt & Whitney.<br><br />
<br />
Submitted by Josephine Rodriguez.<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==A record powerball lottery jackpot==<br />
<br />
On Saturday Oct 22, 2005 the powerball lottery had a record powerball jackpot of 340 million dollars. <br />
<br />
When you buy a ticket for this lottery, you specify five distinct numbers from 1 to 55, which we call basic numbers and one number from 1 to 42 called the bonus number. To win the Jackpot your 5 basic numbers and your bonus number must agree with a random choice of 5 basic numbers and one bonus number chosen by the lottery officials. The number of possible tickets is:<br />
<br />
<center><math>{55 \choose 5} 42 = </math> 146,107,962</center><br />
<br />
Thus if you buy a single ticket, the probability of having a winning jackpot ticket is<br />
<br />
<center> <math>{1} \over {146107962}</math> = .000000006844...</center><br />
<br />
The powerball website and the media expresses this by saying that the odds that you have a winning jackpot ticket is 1 in 146,107,962. <br />
<br />
Whenever there is a record jackpot, the news writers look for suggestions for other rare events that might be more familiar to its readers. <br />
<br />
Our own favorite was suggested by Fred Hoppe: if you toss a coin 27 times your chance of getting 27 heads in a row is greater than your chance of having a winning jackpot ticket when you buy a single ticket. (<math> 2^{27} = 134217728</math> and so there are 134,217,728 possible sequences of heads and tails and only 1 has all heads.)<br />
<br />
In an article for the ''Omaha World-Herald'' Oct 18, 2005 , Robynn Tysver writes:<br />
<br />
<blockquote> You have a greater chance of getting killed by lightning than winning this week's 340 million Powerball jackpot. You also have a greater chance of drowning in a bathtub. The lifetime odds of getting killed by lightning are one in 56,439, and the lifetime odds of dying while in or falling into a bathtub are one in 10,582, according to the National Safety Council. <br />
</blockquote><br />
<br />
These are not even in the ballpark. The ''Minneapolis Star Tribune'' consulted mathematicians David Bressoud and Douglas Arnold who contributed the following:<br />
<br />
According to Arnold you have a seven times better chance of becoming a saint. And Bressoud notes that you're six times more likely to get elected president of the United States. But they also provide the following more interesting estimates:<br />
<br />
<blockquote>Bressoud: "If you buy 10 tickets a week, every week, it would take you 280,000 years before you could expect to win."<br><br><br />
<br />
Arnold: "If you were to select a group of Powerball numbers every minute for 138 years, you would have about a 50 percent chance of picking the winning Powerball ticket." <br><br><br />
<br />
It is not clear what Bressoud means by "expect to win". We can check this by a simple calculation (simple for Mathematica). Let q(n) be the probability that you if you buy n tickets you fail to get a winning jackpot ticket . Then:<br />
<br />
<center> <math> \left(\frac{146107961}{146107962}\right) ^n = q(n) </math></center><br />
<br />
The average number of weeks in a year is 52.177457 so If you buy 10 tickets a week, every week for 280,000 years you will buy about 146,097,000 tickets. Using this number for n in our formula we find that you have about a 37% chance of not getting a winning lottery ticket or a 63% chance of getting one. We would not "expect to win" with a 63% chance of winning but others may. Using our formula for q(n) we find that if we buy 10 tickets a week, every week for 830,000 years you will have about a 95% chance of getting at least one winning lottery ticket which seems to us more appropriate for expecting to win. <br />
<br />
Consider now Arnold's example. Our colleague Dana Williams found that you need to buy a ticket for about 101 million lottery offerings to have about a 50% chance of getting at least one winning lottery ticket. There are an average of 525,946.766 minutes in a year. Dividing 101 million by this number gives 192.035. Thus Arnold's 138 years should be 192 years.<br />
<br />
We asked Professor Arnold about this and he replied:<br />
<br />
<blockquote> That number, which was quoted in the ''Star Tribune'' was an off-the-top-of-my-head calculation made when the reporter called me on<br />
the phone with no warning. Right ballpark, but not very accurate. Later I redid the calculation carefully.</blockquote><br />
<br />
Arnold's computations were similar to ours but he used a greater accuracy for the number of independent lotteries you have to buy to have a 50% chance of choosing the jackpot numbers at least once. His answer to this was 101,274,322. Using this, Arnold's estimate for the number of years, buying a ticket every minute, to have a 50% chance of winning a jackpot is193 years instead of our estimate of 192 years.<br />
<br />
Arnold said that he also estimated the expected value of a $1 ticket. To do this he needed an estimate for the number of tickets sold. He was told that a reasonable estimate was 106 million. In calculating the expected value of a $1 ticket he used the cash value of 164.4 million dollars instead of the annuity payout of 340 million dollars. He also took into account the possibility of having to share the jackpot. Doing this he got an expected value of exactly $1, just the price of the ticket. He commented that if he took into account the taxes the expected value would be more like 80 cents making even this lottery an unfavorable event.<br />
<br />
The news writers also gave a lot of coverage of Senator Gregg (Chairman of the Senate Budget Committee) winning $853,492 for getting the second highest prize: getting the 5 basic numbers correct but note the bonus number. Normally the prize for getting this is $200,000 cash but Gregg was the beneficiary of recent change in the powerball lottery. <br />
<br />
The powerball officials have found that increasing the size of the jackpot can increase the ticket sales because of the public's interest in large jackpots. They do this by increasing the number of possible basic numbers. When they started in 1992, to get the jackpot you had to get the 5 basic numbers chosen from 45 numbers and the 1 bonus number chosen from 45 number correct. Here are the changes so far<br />
<br />
<center><br />
1992 5 of 45 1 of 45<br><br />
1997 5 or 49 1 of 42<br><br />
2002 5 of 55 1 of 42<br><br />
2005 5 of 55 1 of 42<br><br />
</center><br />
<br />
While the lottery officials want to have higher jackpots, they also do not want too long a period between jackpots. Normally the increase in the size of the lottery, when no one wins the jackpot, is determined by the amount taken in in this unsuccessful drawing. This was recently changed so that, when a new record jackpot occurs and no-one wins it, at most 25 million dollars are added to the Jackot until someone wins the jackpot. The money save by this is added to the second prize.<br />
<br />
When the 340 million jackpot was won, 49 players had the five basic numbers correct but not the bonus numbers. For these winners the $200,000 prize had 653,492 added to their prize so they each won $853,492. If they chosen the Powerball play option for an extra $1 their $200,000 would have been multiplied by 2,3,4, or 5 with equal probabilities. Thus if Gregg had chosen the Powerball play option, and been lucky, he would have won 1,653,492 dollars that he could add to his 15 or so million dollars he has in stocks. <br />
<br />
===DISCUSSION===<br />
<br />
(1) Do you think it is fair to advertise the lottery prize as 340 million when the cash prize is only 164.4 million?<br />
<br />
(2) What is the probability of winning the second prize?<br />
<br />
(3) Assuming that the estimate 106 million for the number of tickets sold find the expected number of second prize winners.<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Mammograms Validated as Key in Cancer Fight==<br />
<br />
The ''New York Times'' [http://www.nytimes.com/2005/10/27/health/27breast.html reported] on October 27, 2005 on a new National Cancer Institute study that attributed a significant decrease in the death rate from breast cancer to mammogram screening tests. The study, published in the New England Journal of Medicine, found that from 28% to 65% of the sharp 24% decrease in breast cancer death rates from 1990 to 2000 was due to screening; the remainder was attributed to new drugs used to treat the disease.<br />
<br />
Prior to this study, the value of mammogram screening had been disputed, for several reasons. In the general population, the test results in a large proportion number of false positives, about 90%. Thus, many women who are cancer-free are subjected to unnecessary procedures. Also, approximately 30% of cancers that are detected and treated would not have progressed significantly. Unfortunately, it isn't possible to distinguish between these so-called ''indolent'' cancers and those that become life-threatening, so it is routine practice to treat them all.<br />
<br />
The new study suggests that the benefits of routine mammography are more certain than earlier believed, according to Don Berry, Chairman of the biostatistics department of M. D. Anderson Cancer Center, in Houston, Texas, and the lead author of the paper. He said that the new study for the first time properly separates the effects of therapy and screening. Nonetheless, he cautioned that mammography does pose risks, and recommended that women be counselled before screening.<br />
<br />
Contributed by Bill Jefferys<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div></div>Nano12https://www.causeweb.org/wiki/chance/index.php?title=Chance_News_7&diff=1562Chance News 72005-11-05T09:35:29Z<p>Nano12: /* Learning to speak via statistics and graph theory */</p>
<hr />
<div>Sept 26 2005 to Oct 15 2005<br />
==Quotation==<br />
<blockquote><br />
While writing my book [Stochastic Processes] I had an argument with Feller [Introuction to Probability Theory and its Applications]. He asserted that everyone said "random variable" and I asserted that everyone said "chance variable." We obviously had to use the same name in our books, so we decided the issue by a stochastic procedure. That is, we tossed for it and he won. </blockquote><br />
<br />
<p align = right> Joe Doob<br><br />
[http://www.dartmouth.edu/~chance/Doob/conversation.html Statistical Science]<br><br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Forsooth==<br />
<br />
Peter Winkler suggested our first forsooth.<br />
<br />
<blockquote>Texas beats Ohio State in their opening game <br />
of the season (Saturday Sept 10 2002). The sportscasters (legendary Brent Musburger on play-by-play or Gary Danielson on analysis) observed that of the 14 teams who have <br />
previously played in the championship game (at the end of each season) 5 <br />
have suffered an earlier defeat. "Thus," they conclude, "Ohio State can <br />
still make it to the championship game, but their chances are now less <br />
than 50%."</blockquote><br />
<br />
===Discussion===<br />
<br />
What is wrong with this?<br />
----<br />
Here are forsooths from the September 2005 issues of RSS NEWS<br />
<br />
<blockquote>'Big ticket quiz' at the start of Wimbledon:<br><br><br />
Q. How many punnets (a small light basket or other container for fruit or vegetables) of strawberries are eaten each day during the Wimbledon tournament?<br><br />
Is it (a) over 8,000, (b) over 9,000 or (c) over 10,000?</blockquote><br />
<br />
<div align="right">BBC radio 5<br><br />
20 June 2005</div><br />
<br />
<blockquote>Waiting time for foot surgery down by 500%</blockquote><br />
<br />
<div align="right">Evening News (Edinburgh)<br><br />
5 July 2005</div><br />
<br />
The next two forsooths are from the October RSS news.<br />
<br />
<blockquote>In 1996-8 when the number attending university was static, the participation of women was also static, but male participation fell.</blockquote><br />
<br />
<div align="right">The Times Higher<br><br />
21 January 2005</div><br />
<br />
<blockquote>[On the subject of congestion on the London Underground..] 'Last year 976 million of us used the tube...'</blockquote><br />
<br />
<div align="right">BBC London News<br><br />
19 May 2005</div><br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Fortune's Formula==<br />
<br />
''Fortune's Formula: Wanna Bet?''<br><br />
''New York Times Book Section'', September 25, 2005<br><br />
David Pogue<br />
<br />
This must be the kind of review that every Science writer dreams of. Pogue ends his review with:<br />
<br />
<blockquote> ''Fortune's Formula'' may be the world's first history book, gambling primer, mathematics text, economics manual, personal finance guide and joke book in a single volume. Poundstone comes across like the best college professor you ever had, someone who can turn almost any technical topic into an entertaining and zesty lecture. But every now and then, you can't help wishing there were some teaching assistants on hand to help.</blockquote><br />
<br />
The author William Poundstone is a science writer who has written a number of very successful science books. His book, ''Prisoner's dilemma: John von Neumann, game theory and the puzzle of the bomb'', was written in the style of this book. Indeed Helen Joyce, in her review of this book in Plus Magazine writes:<br />
<br />
<blockquote>This book is a curious mixture of biography, history and mathematics, all neatly packaged into an entertaining and enlightening read. </blockquote><br />
<br />
Poundstone describes himself as a visual artist who does books as a "day job.". You can learn about his art work [http://www.uiowa.edu/~iareview/tirweb/feature/poundstone/interview2.htm here].<br />
<br />
''Fortune's Formula'' is primarily the story of Edward Thorp, Claude Shannon, and John Kelly and their attempt to use mathematics to make money gambling in casinos and on the stock market. None of these did their graduate work in mathematics. Thorp and Kelly got their Phd's in physics and Shannon in Genetics. <br />
<br />
In the spring of 1955, while a graduate student at UCLA, Thorp joined a discussion on the possiblity of making money from roulette. Thorp suggested that they could taking advantage of the fact that bets are still accepted for a few second after the croupier releases the ball, and in these seconds, he could estimate what part of the wheel the ball would stop. <br />
<br />
Thorp did not pursue this and in 1959 became an instructor in mathematics at M.I.T. Here he became interested in blackjack and developed his famous card counting method for wining at blackjack. He decided to publish his method in the most prestigious journal he could find and settled on ''Proceedings of the National Academy of Sciences''. For this he needed to have a member of the Academy submit his paper. The only member in the math department was Shannon so he had to persuade him of the importance of his paper. Shannon not only agreed but in the process became fascinated by Thorp's idea for beating roulette. He agreed to help Thorp carry this out. They built a roulette machine in Shannon's basement. It worked fine there in trial runs but not so well in the casino so they did not pursue this method of getting rich. <br />
<br />
Of course Thorp is best known for showing that blackjack is a favorable game and giving a method to exploit this fact. Shannon is best known for his work in information theory. Kelly is known his method for gambling in a favorable game. This plays a central role in Poundstone's book and is probably why Pogue felt that it would help if he had a teaching assistant. Poundstone tries to explain Kelly's work in many different ways but what he really needed to understand it is an example but this required too many formulas for a popular book. So we shall include an example from Chance News 7.09. <br />
<br />
Writing for Motley Fool, 3 April 1997 Mark Brady complained about the inumeracy of the general public and gave a number of examples including this one:<br />
<br />
<blockquote> Fear of uncertainty and innumeracy are synergistic. Most people cannot do the odds. What is a better deal over a year? A 100% safe return with 5 percent interest or a 90 percent safe return with a 20 percent return. For the first deal, your return will be 5% percent. For the second, your return will be 8%. Say you invest $1000 10 times. Your interest for the 9 successful deals will be 9000 x 0.2 or 1800. Subtract the 1000 you lost on the 10th deal and you get a $800 return on your original $10,000 for 8 percent.</blockquote><br />
<br />
Peter Doyle suggested that a better investment strategy in this case is:<br />
<br />
Faced with a 100 percent-safe investment returning 5 percent and a 90 percent-safe investment returning 20%, you should invest 20% of your funds in the risky investment and 80% in the safe investment. This gives you an effective return of roughly 5.31962607969968292 percent. <br />
<br />
Peter is using a money management system due to J. L. Kelly (1956: "A new interpretation of information rate," ''Bell System Technical Journal'', '''35'''). Kelly was interested in finding a rational way to invest your money faced with one or more investment schemes, each of which has a positive expected gain. He did not think it reasonable to try simply to maximize your expected return. If you did this in the Motley Fools example as suggested by Mark Brady, you would choose the risky investment and might well lose all your money the first year. We will illustrate what Kelly did propose in terms of Motley Fools example. <br />
<br />
We start with an initial capital, which we choose for convenience to be $1, and invest a fraction r of this money in the gamble and a fraction 1-r in the sure-thing. Then for the next year we use the same fractions to invest the money that resulted from the first year's investments and continue, using the same r each year. Assume, for example, that in the first and third years we win the gamble and in the second year we lose it. Then after 3 years our investment returns an amount f(r) where: <br />
<br />
<math><br />
f(r) = (1.2r + 1.05(1-r))(1.05(1-r))(1.2r + 1.05(1-r)). <br />
</math><br />
<br />
After n years, we would have n such factors, each corresponding to a win or a loss of our risky investment. Since the order of the terms does not matter our capital will be: <br />
<br />
<math><br />
f(r,n) = (1.2r + 1.05(1-r))^W(1.05(1-r))^L<br />
</math><br />
<br />
where W is the number of times we won the risky investment and L the number of times we lost it. Now Kelly calls the quantity:<br />
<br />
<math><br />
G(r) =\lim_{n \to \infty }\frac{\log(f( r,n)} {n}<br />
</math> <br />
<br />
the exponential rate of growth of our capital. In terms of G(r) our capital should grow like <math> e^{G(r)} </math>. In our example: <br />
<br />
<math><br />
\log(\frac{f(r,n)}{n}) = \frac{W}{n}\log(1.2r + 1.05(1-r)) + \frac{L}{n}\log(1.05(1-r))<br />
</math> <br />
<br />
Since we have a 90% chance of winning our gamble, the [http://en.wikipedia.org/wiki/Strong_law_of_large_numbers#The_strong_law strong law of large numbers] tells us that as n tends to infinity this will converge to <br />
<br />
<math><br />
G(r) = 0.9\log(1.2r + 1.05(1-r))+0.1\log(1.05(1-r))<br />
</math><br />
<br />
It is a simple calculus problem to show that G(r) is maximized by r = 0.2 with: <br />
G(0.2) = 0.05183. Then e^{0.05183} = 1.0532, showing that our maximum rate of growth is 5.32% as claimed by Peter. <br />
<br />
The attractiveness of the Kelly investment scheme is that, in the long run, any other investment strategy (including those where you are allowed to change your investment proportions at different times) will do less well. "In the long run and less well" means more precisely that the ratio of your return under the Kelly scheme and your return under any other strategy will tend to infinity.<br />
<br />
Thorp had a very good experience in the stock market, which is described very well by Gaeton Lion in his excellent [http://www.amazon.com/gp/product/customer-reviews/0809046377/ref=cm_cr_dp_pt/103-8647004-5865443?%5Fencoding=UTF8&n=283155&s=books review] of ''Fortune's Formula''. He writes:<br />
<br />
<blockquote> Ed Thorp succeeded in deriving superior returns in both gambling and investing. But, it was not so much because of Kelly's formula. He developed other tools to achieve superior returns. In gambling, Ed Thorp succeeded at Black Jack by developing the card counting method. He just used intuitively Kelly's formula to increase his bets whenever the odds were in his favor. Later, he ran a hedge fund for 20 years until the late 80s and earned a rate of return of 14% handily beating the market's 8% during the period. <br><br><br />
<br />
Also, his hedge fund hardly lost any value on black Monday in October 1987, when the market crashed by 22%. The volatility of his returns was far lower than the market. He did this by exploiting market inefficiencies using warrants, options, and convertible bonds. The Kelly formula was for him a risk management discipline and not a direct source of excess return. </blockquote><br />
<br />
Shannon also made a lot of money on the stock market, but did not use Kelly's formula. In his [http://www.amazon.com/gp/product/customer-reviews/0809046377/ref=cm_cr_dp_pt/103-8647004-5865443?%5Fencoding=UTF8&n=283155&s=books review] Gaeton Lion writes<br />
<br />
<blockquote>Claude Shannon amassed large wealth by recording one of the best investment records. His performance had little to do with Kelly's formula. Between 1966 and 1986, his record beat even Warren Buffet (28% to 27% respectively). Shannon strategy was similar to Buffet. Both their stock portfolios were concentrated, and held for the long term. Shannon achieved his record by holding mainly three stocks (Teledyne, Motorola, and HP). The difference between the two was that Shannon invested in technology because he understood it well, while Buffet did not. </blockquote><br />
<br />
Finally, Thorp provided the following comments for the book cover:<br />
<br />
<blockquote>From bookies to billionaires, you'll meet a motley cast of characters in this highly original, 'outside the box' look at gambling and investing. Read it for the stories alone, and you'll be surprised at how much else you can learn without even trying. --Edward O. Thorp, author of ''Beat the Dealer'' and ''Beat the Market''.</blockquote><br />
<br />
Submitted by Laurie Snell.<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Which foods prevent cancer?==<br />
<br />
Which of these foods will stop cancer? (Not so fast)<br><br />
New York Times, 27 September 2005, Sect. F, p. 1<Br><br />
Gina Kolata<br />
<br />
Among other examples, the article includes a [http://www.nytimes.com/imagepages/2005/09/26/science/20050927_CANCER_GRAPHIC.html data graphic] on purported benefits of dietary fiber in preventing colorectal cancer. Early observational studies indicated an association, but subsequent randomized experiments found no effect. <br />
<br />
More to follow.<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Slices of risk and the <em>broken heart</em> concept==<br />
[http://www.gloriamundi.org/picsresources/news20050912.pdf How a Formula Ignited Market That Burned Some Big Investors],<br />
Mark Whitehouse, The Wall Street Journal, September 12, 2005.<br><br />
<br />
This on-line article relates how a statistician, David Li,<br />
unknown outside a small coterie of finance theorists, helped change the world of investing. <br />
<br />
The article focuses on a event last May when General Motors Corp's debt<br />
was downgraded to junk status, causing turmoil in some financial markets.<br />
The article gives a nice summary of the underlying financial instruments known<br />
as credit derivatives -<br />
investment contracts structured so their value depends on the behavior of some other thing or event -<br />
with exotic names like <br />
[http://en.wikipedia.org/wiki/Collateralized_debt_obligations collateralized debt obligations] and [http://en.wikipedia.org/wiki/Credit_default_swap credit-default swaps].<br />
<br />
The critical step is to estimate the likelihood that many of the companies <br />
in a pool of companies would go bust at once. <br />
For instance, if the companies were all in closely related industries,<br />
such as auto-parts suppliers, they might fall like dominoes after a catastrophic event.<br />
Such a pool would have a 'high default correlation'.<br />
<br />
In 1997, nobody knew how to calculate default correlations with any precision. <br />
Mr. Li's solution drew inspiration from a concept in actuarial science known as the <br />
<em>broken heart</em> syndrome - people tend to die faster after the death of a beloved spouse. <br />
Some of his colleagues from academia were working on a way to predict this<br />
death correlation, something quite useful to companies that sell life insurance and joint annuities.<br />
He says:<br />
<blockquote><br />
Suddenly I thought that the problem I was trying to solve was exactly like the problem these<br />
guys were trying to solve,.<br />
Default is like the death of a company, so we should<br />
model this the same way we model human life."<br />
</blockquote><br />
<br />
This gave him the idea of using [http://en.wikipedia.org/wiki/Copula_%28statistics%29 copulas], <br />
mathematical functions the colleagues had begun applying to actuarial science. <br />
Copulas help predict the likelihood of various events<br />
occurring when those events depend to some extent on one another. <br />
Until the events last May of this year, one of the most popular copulas for bond pools <br />
was the Gaussian copula, named after <br />
[http://en.wikipedia.org/wiki/Carl_Friedrich_Gauss Carl Friedrich Gauss], a 19th-century German statistician. <br />
<br />
===Further reading===<br />
* The [http://www.gloriamundi.org/picsresources/news20050912.pdf on-line article] gives more details about what went wrong in the financial markets in May and the search for a more appropriate copula to capture better the <em>broken heart</em> syndrome between companies.<br />
* [http://en.wikipedia.org/wiki/Wikipedia Wikipedia] is a very worthwhile on-line resource for definitions of technical words, such as [http://en.wikipedia.org/wiki/Copula_%28statistics%29 copula].<br />
<br />
Submitted by John Gavin.<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Learning to speak via statistics and graph theory==<br />
<br />
[http://education.guardian.co.uk/tefl/teaching/story/0,15085,1576100,00.html Computer learns grammar by crunching sentences], Max de Lotbinière September 23, 2005, [http://www.guardianweekly.co.uk/ Guardian Weekly].<br><br />
[http://www.cornellsun.com/vnews/display.v/ART/2005/09/09/432118a84f6af Profs’ New Software ‘Learns’ Languages], Ben Birnbaum, 9 Sep 2005, Cornell Daily Sun.<br />
<br />
A language-learning robot may sound like science fiction but new software, developed by Cornell University psychology professor Shimon Edelman, with colleagues Zach Solan, David Horn and Eytan Ruppin from Tel Aviv University in Israel, is well on the way to constructing a computer program that can teach itself languages and make up its own sentences, the developers' claim.<br />
<br />
Unlike previous attempts at developing computer algorithms for language learning - "Automatic Distillation of Structure," or "ADIOS" for short - discovers complex patterns in raw text by repeatedly aligning sentences and looking for overlapping parts.<br />
Once it has derived a language's rules of grammar,<br />
it can then produce sentences of its own, simply from blocks of text in that language.<br />
<br />
It has been evaluated on artificial context-free grammars with thousands of rules, <br />
on natural languages as diverse as English and Chinese, <br />
on coding regions in DNA sequences and on protein data correlating sequence with function. <br />
<br />
Edelman comments:<br />
<blockquote><br />
Adios relies on a statistical method for pattern extraction and on structured generalisations <br />
- the two processes that have been implicated in language acquisition.<br />
Our experiments show that Adios can acquire intricate structures <br />
from raw data including transcripts of parents' speech directed at two- or three-year-olds.<br />
This may eventually help researchers understand how children, <br />
who learn language in a similar item-by-item fashion, and with little supervision, <br />
eventually master the full complexity of their native tongue.<br />
</blockquote><br />
<br />
[http://plus.maths.org/latestnews/may-aug05/adios/ Plus Magazine's website]<br />
offers a more logical explanation:<br />
<blockquote><br />
The ADIOS algorithm is based on statistical and algebraic methods performed on one of the most basic and versatile objects of mathematics - the graph.<br />
Given a text, the program loads it as a graph by representing each word by a node, or vertex, and each sentence by a sequence of nodes connected by lines. A string of words in the text is now represented by a path in the graph. <br><br />
<br />
Next it performs a statistical analysis to see which paths, or strings of words, occur unusually often. <br />
It then decides that those that appear most frequently - called "significant patterns" - <br />
can safely be regarded as a single unit<br />
and replaces the set of vertices in each of these patterns by a single vertex, <br />
thus creating a new, generalised, graph.<br><br />
<br />
Finally, the program looks for paths in the graph which just differ by one vertex. <br />
These stand for parts of sentences that just differ by one word (or compound of words) like "the cat is hungry" and "the dog is hungry". <br />
Performing another statistical test on the frequency of these paths, the program identifies classes of vertices, or words, that can be regarded as interchangeable, or equivalent. <br />
The sentence involved is legitimate no matter which of the words in the class - in our example "cat" or "dog" - you put in.<br><br />
<br />
This last step is then repeated recursively.<br><br />
</blockquote><br />
<br />
[http://plus.maths.org/latestnews/may-aug05/adios/ The website] uses graphs to illustrate some examples and it finishes with some reassuring words:<br />
<blockquote><br />
All this doesn't mean, of course, that the program actually "understands" what it's saying. It simply knows how to have a good go at piecing together fragments of sentences it has identified, in the hope that they are grammatically correct. So if, like me, you're prone to swearing at your computer, you can safely continue to do so: it won't answer back for a long while yet.<br />
</blockquote><br />
<br />
===Further reading===<br />
The [http://adios.tau.ac.il/ ADIOS homepage] offers an overview and more detailed description of the program.<br />
<br />
Submitted by John Gavin.<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Understanding probability==<br />
<br />
Understanding Probability:Chance rules in everyday life<br><br />
Cambridge University Press 2004<br><br />
Henk Tijms<br />
<br />
Hank Tijms is Professor in Operation Research at the Vrije University in Amsterdam. This book is based on his earlier Dutch book “Spelen met Kansen.” <br />
<br />
The aim of this book is to show how probability applies to our everyday life in a way that your Uncle George could understand even if he has forgotten much of his high school math. Tijms does not try to avoid mathematics but only to postpone the formal math until the reader has seen the many applications of probability in the real world, how much fun it is, and learned to work problems and when he can’t work one how to get the answer by simulation. He learns all this in part I of the book and then he learns the more formal math in Part II.<br />
<br />
In Chapter 1 Tijms asks the reader to think about problems with surprising answers in the spirit of Susan Holmes “[http://www-stat.stanford.edu/~susan/surprise/ Probability by Surprise]” including the birthday problem and the Monty Hall problem. Readers are on their own to try to solve one or more of the problems but promised that they will see the solutions later in the book. <br />
<br />
Chapter 2 deals with the law of large numbers and introduces the concept of simulation. This theorem is explained and illustrated by problems related, for example, to coin tossing, random walks and casino games. Expected value is introduced in an informal way to be defined more carefully later in the book. For the reader who is not frightened by mathematical formulas, Tijms includes a discussion of the Kelly betting system with a footnote saying that this paragraph can be skipped at first reading. This is a fascinating topic that is widely applied in gambling and stock investment but rarely appears in a probability book.<br />
<br />
In Chapter 3 the author returns to previous problems such as the birthday problem and gambling systems and solves them first by simulation and then by mathematics. <br />
<br />
In this chapter Tijms describes Efron’s bootstrap method and uses it to solve a number of problems including a hypothetical clinical trial and to test if the famous 1970 draft lottery during the Vietnam War was fair. Again the bootstrap method has wide application but rarely occurs in an elementary probability or statistics book.<br />
<br />
Chapter 4 describes the binomial, Poisson, and hypergeomtric distributions and how to use them in solving problems such as the famous hat check problem, and a variety of interesting lottery questions. The Poisson process is discussed but again with the footnote that novice readers might want to read this at a later time.<br />
<br />
Chapter 5 is mainly about Center Limit Theorem and its many applications especially to statistics. <br />
<br />
Chapter 6 introduces Chance trees and Bayes’s rule. The tree method is used to explain a variety of problems including the Monty Hall Problem and the false-positive paradox. <br />
<br />
This is a brief description of the first six chapters which constitute Part I of the book. Now the fun is over. Part 2 called “Essentials of probability” looks like the traditional first chapters in a standard probability book. But the reader has already found how exciting probability is, has a good intuitive idea of the basic concepts and has worked many of the interesting problems at the end of each chapter either using math or simulation. For some students this might allow them to actually enjoy Part 2. But your Uncle George may want to quit while they are ahead. <br />
<br />
Tijms writes with great clarity and his enthusiasm for probability in the real world is contagious. We were delighted to see, as acknowledged in the preface, that Tijms included several of the more interesting problems discussed in Chance News, often going well beyond what we had said in our discussion of the problem. <br />
<br />
This book presents a completely new way to go about teaching a first course in probability and we think those who teach such a course should consider trying it out.<br />
<br />
===Discussion===<br />
<br />
(1) In the days of Basic we required all students to learn Basic in their first math course so we could assume that students could write programs to simulate probability problems and so me made heavy use of simulation as suggested in this book. The author uses Pascal in his book. What present language do you think is easiest for a student with no computing experience to learn?<br />
<br />
We asked Professor Tijms what the situation was in math departments in Europe and he replied:<br />
<br />
<blockquote>In math departments of universities and polytechnic schools in Europe students learn to write computer programs. In my university they still learn to program in Java and C++ ( in previous days Pascal), but I see in the Netherlands the trend that the instructors think it is sufficient if the students are able to program in Matlab. <br><br><br />
<br />
In ny book I have chosen to formulate the simulation programs in Pascal because of the clarity and the simplicity of the language, though this language is hardly used anymore. The introductory probability course at my university is given before they have learned to program, but this does not prevent them of simulating probability problems by using Excel. In the simulation of many elementary probability problems a random-number generator alone suffices to simulate those problems and so Excel can be used. In the second year they have mastered Matlab, a perfect tool with its excellent graphics to simulate many challenging probability problems ( they really like it, in particular when it concerns problems such as the problems 2.24-2.45 in chapter 2 and the problems 5.11-5.13 in chapter 5). <br />
</blockquote><br />
<br />
<br />
(2) Do you think that probability books should include data to test probability models that are said to describe real world problems? If so name some models that you think would pass such a test and some that you think might not.<br />
<br />
Submitted by Laurie Snell<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Societies worse off when they have God on their side==<br />
<br />
[http://www.timesonline.co.uk/article/0,,2-1798944,00.html Societies worse off when they have God on their side]<br><br />
Timesonline, September 27, 2005<br><br />
Ruth Gledhill<br />
<br />
[http://moses.creighton.edu/JRS/2005/2005-11.html Cross-national correlations of quantifiable societal health with popular religiosity and secularism in the prosperous democracies]<br><br />
Journal of Religion & Society, Vol.7(2005)<br><br />
Gregory S. Paul<br />
<br />
In the Times article we read:<br />
<br />
<blockquote>According to the study, belief in and worship of God are not only unnecessary for a healthy society but may actually contribute to social problems.<br><br><br />
Many liberal Christians and believers of other faiths hold that religious belief is socially beneficial, believing that it helps to lower rates of violent crime, murder, suicide, sexual promiscuity and abortion. The benefits of religious belief to a society have been described as its “spiritual capital”. But the study claims that the devotion of many in the US may actually contribute to its ills. <br />
</blockquote><br />
<br />
Gregory Paul is a dinosaur paleontologist and on an [http://www.abc.net.au/worldtoday/indexes/2005/twt_20050928.htm interview] on Australian ABC radio Paul said that, being a paleontologist, for many years he had to deal with the issue of creationism versus evolutionary science in the U.S and his interest in evolutionary science prompted him to look at whether there was any link between the religiosity of a society and how well that society functions. <br />
<br />
If you look at Paul's article you will find very little technical statistical analysis, for example, he did not carry out a regression analysis. Rather he rests his case on the series of scatterplots.<br />
<br />
Paul describes his data sources as:<br />
<br />
<blockquote>Data sources for rates of religious belief and practice as well as acceptance of evolution are the 1993 Environment I (Bishop) and 1998 Religion II polls conducted by the International Social Survey Program (ISSP), a cross-national collaboration on social science surveys using standard methodologies that currently involves 38 nations. The last survey interviewed approximately 23,000 people in almost all (17) of the developed democracies; Portugal is also plotted as an example of a second world European democracy. Results for western and eastern Germany are combined following the regions' populations. England is generally Great Britain excluding Northern Ireland; Holland is all of the Netherlands. The results largely agree with national surveys on the same subjects; for example, both ISSP and Gallup indicate that absolute plus less certain believers in a higher power are about 90% of the U.S. population. The plots include Bible literalism and frequency of prayer and service attendance, as well as absolute belief in a creator, in order to examine religiosity in terms of ardency, conservatism, and activities. </blockquote><br />
<br />
Here are the countries Paul considered with the abbreviations used on the graphics. <br />
<br />
A = Australia, C = Canada, D = Denmark, E = Great Britain, F = France, G = Germany,<br />
H = Holland, I = Ireland, J = Japan, L = Switzerland, N = Norway, P = Portugal, R = Austria,<br />
S = Spain, T = Italy, U = United States, W = Sweden, Z = New Zealand.<br />
<br />
There seems to be no agreement as to which countries are developed democracies. For example Paul might have included Greece and Belgium, Finland, and others but the data may have determined his choice. Paul comments that he added Portugal as an example of a second world democracy. <br />
<br />
Paul's anaysis of the data includes a series of 9 Figures which are available at the end of the article and are the most interesting part of the study. If you try printing Paul's article you will only get the first of his 9 Figures. When you look at the [http://moses.creighton.edu/JRS/2005/2005-11.html web version] you will still see only Figure 1 but the others can be viewed by selecting the numbers from 2 to 9 on the left side of Figure 1.<br />
<br />
Figure 1 deals with the proportion of people who accept human evolution which is interesting but not as relevant to the welfare of the people as others so we will look at Figure 2.<br />
<br />
[[Image:religion2.png|500px|center|Source:Gregory Paul]]<br />
<br />
Each Figure iprovides 5 separate scatterplots. Ïn Figure 2 we see that the U.S. has largest number--between 6 and 7-- of homicides per 100,000 and Spain has the lowest number with less than 1 homicide per 100,000. We also see that the U.S. has the highest proportion of people, about 25%, who take the bible literally while several countries have less than 10% such people.<br />
<br />
What we cannot do is compare the number of homicides per thousand between those who take the bible literally and those who are agnostics or atheists which is what we would really want to know. Presumably the data did not permit this comparison. <br />
<br />
[[Image:religion3.png|500px|center|Source:Gregory Paul]]<br />
<br />
Figure 3 deals with "14-24 year old suicides per 100,000". Here the U.S. is in about the middle.<br />
<br />
Figure 4 deals with the "under-five mortalities per 1000 births".<br />
<br />
[[Image:religion4.png|500px|center|Source:Gregory Paul]]<br />
<br />
Ignoring Portugal, the U.S. has the highest number of under-five mortalities per 1000 births-- between 7 and--8 while several countries have only 4.<br />
<br />
The other figures can be seen at end of Paul's article. They deal with life expectancy, sexually transmitted diseases, abortion and 15-16 year old pregnancies. Life expectancy is the smallest in the U.S. and for sexually transmitted diseases, abortion and 15-17 year old prenacies the U.S. is at the top of the graphs and in fact these look like outliers.<br />
<br />
Well, this study does not by itself justify the Times hedline: "Societies worse off when they have God on their side." Paul himself would not claim this. He writes:<br />
<br />
<blockquote> This study is a first, brief look at an important subject that has been almost entirely neglected by social scientists. The primary intent is to present basic correlations of the elemental data. Some conclusions that can be gleaned from the plots are outlined. This is not an attempt to present a definitive study that establishes cause versus effect between religiosity, secularism and societal health. It is hoped that these original correlations and results will spark future research and debate on the issue.</block<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div></div>Nano12https://www.causeweb.org/wiki/chance/index.php?title=Chance_News_8&diff=1561Chance News 82005-11-05T09:35:26Z<p>Nano12: /* DISCUSSION */</p>
<hr />
<div>Oct 15 to Oct 30<br />
<br />
==Quotation==<br />
<blockquote>One more fagot of these adamantine bandages, is, the new science of Statistics. It is a rule, that the most casual and extraordinary events -- if the basis of population is broad enough -- become matter of fixed calculation. It would not be safe to say when a captain like Bonaparte, a singer like Jenny Lind, or a navigator like Bowditch, would be born in Boston: but, on a population of twenty or two hundred millions, something like accuracy may be had. Ralph Waldo Emerson Fate</blockquote><br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Forsooth==<br />
Here's another Forsooth from the October issue of RSS News.<br />
<blockquote>Your'e more likely to die in a fire in Strathclyde than anywhere else in the country</blockquote><br />
<br />
<div align="right">BBC1 mews bullietin<br><br />
11 May 2005</div><br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==The Poisson distribution and the Supreme Court==<br />
The Poisson distribution and the Supreme Court<br><br />
''Journal of the American Statistical Association'' 31, no. 195 ,(1936), 376-80<br><br />
W. Allen Wallis<br />
<br />
Supreme Court Appointments as a Poisson distribution<br><br />
''American Journal of Political Science'', 26, No.1, February 1982<br><br />
S. Sidney Ulmer<br />
<br />
This is not current news, but since Supreme Court appointments are in the news we felt that these articles might make an interesting class discussion.<br />
<br />
In 1936 statistician Allen Wallis suggested that a Poisson distribution can approximate the number of U.S. Supreme Court appointments in a given year. In his Table 1 Wallis provided the number appointed in each year over the intervals with different numbers of Justices on the Supreme Court: 1790-1806 (6) 1807-1836 (7), and 1837-1932 (9). Actually there were 10 in the years 1963 to 1967 which Wallis called "negligible exceptions."<br />
<br />
[[Image:wallis1.png|500px|center]]<br />
<br />
Wallis then restricts himself to the years 1837-1932 and finds that a Poisson distribution with mean .5 can approximate the number of court appointments in a year. His results are shown in his Figure II:<br />
<br />
[[Image:wallis2.png|500px|center]]<br />
<br />
In his article, Sidney Ulmer updated the data to 1980 and also includes data from the early Supreme Courts with 6 and 7 members. Thus his data covers the years 1790--1980. His Table 1 compares the actual number of appointments in a year with the expected number of appointments assuming a Poisson distribution with mean 5.13.<br />
<br />
[[Image:ulmer1.png|500px|center]]<br />
<br />
In his Table II Ulmer limits the data to the 9 member Supreme Courts: 1837 to 1862 and 1869-1980).<br />
<br />
[[Image:ulmer2.png|500px|center]]<br />
<br />
Testing the goodness of fits, Ulmer argues that the fit with the varying size Supreme Courts is just as good as with fixed size Supreme Courts.<br />
<br />
===DISCUSSION===<br />
<br />
(1) What is the probability that a President will make 2 or more appointments to the Supreme Court during a 4-year term? What is the probability a President makes no appointments during a 4-year term? Has this ever happened?<br />
<br />
(2) Do you agree with Ulmer that there is no reason to limit the data to years with the Supreme Court is the same size?<br />
<br />
(3) Obtain the data needed to update Ulmer's results to today and provide Tables that correspond to Ulmer's Tables 1 and 2. Add your Tables to this Chance News and make your data available to make it easier to update this in future years.<br />
<br />
Contributed by Laurie Snell<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Possible Cancer Cluster in Connecticut==<br />
Pratt Agrees to Increase Funding for Brain Cancer Study <br><br />
''The Associated Press''<br><br />
October 11, 2005<br><br />
Stephen Singer<br><br />
<br />
<br />
In a case that seems eerily familiar to the leukemia cancer cluster made famous by the book and movie, ''A Civil Action'', researchers are trying to determine whether or not a cancer cluster exists among workers at Pratt & Whitney, a company that manufactures jet engines. Over one hundred former or current Pratt & Whitney employees have been identified as having a relatively rare type of fatal brain tumor known as glioblastoma multiforme, which strikes 3 people per 100,000 every year. Many of these workers have been exposed to metals and chemical substances, including TCE (trichloroethylene), which is an engine degreaser. TCE is the same carcinogenic chemical that was dumped in the 1960’s and 1970’s by the chemical company, WR Grace, in Woburn, MA, and that was found to have contaminated the drinking water in two of the town’s wells. <br><br />
<br />
<br />
Prior to the recent announcement that the funding is being increased from $6 million dollars to $12 million dollars, this medical study was already being described as the largest occupational health study ever conducted. It covers 250,000 people who worked at any of the seven Connecticut Pratt & Whitney plants from 1952 to 2001. So far, at least 125 cases of brain cancer have been documented, according to the lawyer who represents dozens of individuals and family members.<br><br />
<br />
<br />
The study falls under the auspices of the Connecticut Department of Public Health. However, due to the overwhelming cost and scope of the study, Pratt & Whitney is funding the project. Since Pratt is paying for the study, they chose the researchers, a team from the University of Pittsburgh. The project began three years ago, and the results are expected to be available between 2007 and 2009.<br><br />
<br />
<br />
In the meantime, this case faces many of the obstacles common in the quest to establish whether or not a cancer cluster exists, such as proving causation, the fact that it can take a long time (sometimes 5-40 years) after exposure for true problems to show up, and finding the people who were exposed & convincing them to participate in the study. Additionally, there are legal difficulties for the families involved, including Connecticut’s statute of limitations laws, the length of time it takes investigators to reach a conclusion, the cost of litigation, and the “deep pockets” of a company like Pratt & Whitney.<br><br />
<br />
<br />
This case study provides a current example of an ongoing investigation into a possible cancer cluster. Will it ultimately be found to be a coincidence cluster or proven to be a true cancer cluster? Does it make sense that the researchers are including in the study everyone who worked at Pratt over a fifty year period, even those who only worked there for a brief time period and those who were not directly exposed to toxic substances (i.e. office workers)? Could the researchers possibly have an unconscious bias in favor of the company that is funding their research? If the company doesn’t fund the research, then who should? Is there some other way to structure such investigations, so that the company involved pays for the study, but is not allowed to choose the researchers and directly fund them?<br><br />
<br />
<br />
'''Further Reading'''<br><br />
<br />
• “Rare Cancer Found in Workers”, ''The New York Times'', March 10, 2002, Jane Gordon<br><br />
• “Scientist: Pratt Commits to Cancer Study”, ''The Hartford Courant'', May 19, 2005<br><br />
• “Participation in Cancer Study at Pratt Lagging”, ''The Hartford Courant'', October 12, 2005, Paul Marks<br><br />
• ''The New Haven Advocate'' has had more than a dozen articles that explain the working conditions at Pratt & Whitney, and also chronicle the history & progression of this case. These articles have been investigated and written primarily by Carole Bass, Associate Editor. A few of the articles are listed below. <br> <br />
-“Worked to Death”, August 2, 2001, Carole Bass & Camille Jackson<br><br />
-“Talking Cure”, October 28, 2004, Dave Goldberg<br><br />
-“Time’s Not on Their Side”, January 20, 2005, Carole Bass<br><br />
-“The Brains Behind the Brain”, October 20, 2005, Carole Bass <br><br />
For the early New Haven Advocate articles (i.e., 2001-2002) on this subject, go to http://old.newhavenadvocate.com/workedtodeath/index.html<br> <br />
For the articles since 2002, go to <br><br />
http://www.newhavenadvocate.com and search for Pratt & Whitney.<br><br />
<br />
Submitted by Josephine Rodriguez.<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==A record powerball lottery jackpot==<br />
<br />
On Saturday Oct 22, 2005 the powerball lottery had a record powerball jackpot of 340 million dollars. <br />
<br />
When you buy a ticket for this lottery, you specify five distinct numbers from 1 to 55, which we call basic numbers and one number from 1 to 42 called the bonus number. To win the Jackpot your 5 basic numbers and your bonus number must agree with a random choice of 5 basic numbers and one bonus number chosen by the lottery officials. The number of possible tickets is:<br />
<br />
<center><math>{55 \choose 5} 42 = </math> 146,107,962</center><br />
<br />
Thus if you buy a single ticket, the probability of having a winning jackpot ticket is<br />
<br />
<center> <math>{1} \over {146107962}</math> = .000000006844...</center><br />
<br />
The powerball website and the media expresses this by saying that the odds that you have a winning jackpot ticket is 1 in 146,107,962. <br />
<br />
Whenever there is a record jackpot, the news writers look for suggestions for other rare events that might be more familiar to its readers. <br />
<br />
Our own favorite was suggested by Fred Hoppe: if you toss a coin 27 times your chance of getting 27 heads in a row is greater than your chance of having a winning jackpot ticket when you buy a single ticket. (<math> 2^{27} = 134217728</math> and so there are 134,217,728 possible sequences of heads and tails and only 1 has all heads.)<br />
<br />
In an article for the ''Omaha World-Herald'' Oct 18, 2005 , Robynn Tysver writes:<br />
<br />
<blockquote> You have a greater chance of getting killed by lightning than winning this week's 340 million Powerball jackpot. You also have a greater chance of drowning in a bathtub. The lifetime odds of getting killed by lightning are one in 56,439, and the lifetime odds of dying while in or falling into a bathtub are one in 10,582, according to the National Safety Council. <br />
</blockquote><br />
<br />
These are not even in the ballpark. The ''Minneapolis Star Tribune'' consulted mathematicians David Bressoud and Douglas Arnold who contributed the following:<br />
<br />
According to Arnold you have a seven times better chance of becoming a saint. And Bressoud notes that you're six times more likely to get elected president of the United States. But they also provide the following more interesting estimates:<br />
<br />
<blockquote>Bressoud: "If you buy 10 tickets a week, every week, it would take you 280,000 years before you could expect to win."<br><br><br />
<br />
Arnold: "If you were to select a group of Powerball numbers every minute for 138 years, you would have about a 50 percent chance of picking the winning Powerball ticket." <br><br><br />
<br />
It is not clear what Bressoud means by "expect to win". We can check this by a simple calculation (simple for Mathematica). Let q(n) be the probability that you if you buy n tickets you fail to get a winning jackpot ticket . Then:<br />
<br />
<center> <math> \left(\frac{146107961}{146107962}\right) ^n = q(n) </math></center><br />
<br />
The average number of weeks in a year is 52.177457 so If you buy 10 tickets a week, every week for 280,000 years you will buy about 146,097,000 tickets. Using this number for n in our formula we find that you have about a 37% chance of not getting a winning lottery ticket or a 63% chance of getting one. We would not "expect to win" with a 63% chance of winning but others may. Using our formula for q(n) we find that if we buy 10 tickets a week, every week for 830,000 years you will have about a 95% chance of getting at least one winning lottery ticket which seems to us more appropriate for expecting to win. <br />
<br />
Consider now Arnold's example. Our colleague Dana Williams found that you need to buy a ticket for about 101 million lottery offerings to have about a 50% chance of getting at least one winning lottery ticket. There are an average of 525,946.766 minutes in a year. Dividing 101 million by this number gives 192.035. Thus Arnold's 138 years should be 192 years.<br />
<br />
We asked Professor Arnold about this and he replied:<br />
<br />
<blockquote> That number, which was quoted in the ''Star Tribune'' was an off-the-top-of-my-head calculation made when the reporter called me on<br />
the phone with no warning. Right ballpark, but not very accurate. Later I redid the calculation carefully.</blockquote><br />
<br />
Arnold's computations were similar to ours but he used a greater accuracy for the number of independent lotteries you have to buy to have a 50% chance of choosing the jackpot numbers at least once. His answer to this was 101,274,322. Using this, Arnold's estimate for the number of years, buying a ticket every minute, to have a 50% chance of winning a jackpot is193 years instead of our estimate of 192 years.<br />
<br />
Arnold said that he also estimated the expected value of a $1 ticket. To do this he needed an estimate for the number of tickets sold. He was told that a reasonable estimate was 106 million. In calculating the expected value of a $1 ticket he used the cash value of 164.4 million dollars instead of the annuity payout of 340 million dollars. He also took into account the possibility of having to share the jackpot. Doing this he got an expected value of exactly $1, just the price of the ticket. He commented that if he took into account the taxes the expected value would be more like 80 cents making even this lottery an unfavorable event.<br />
<br />
The news writers also gave a lot of coverage of Senator Gregg (Chairman of the Senate Budget Committee) winning $853,492 for getting the second highest prize: getting the 5 basic numbers correct but note the bonus number. Normally the prize for getting this is $200,000 cash but Gregg was the beneficiary of recent change in the powerball lottery. <br />
<br />
The powerball officials have found that increasing the size of the jackpot can increase the ticket sales because of the public's interest in large jackpots. They do this by increasing the number of possible basic numbers. When they started in 1992, to get the jackpot you had to get the 5 basic numbers chosen from 45 numbers and the 1 bonus number chosen from 45 number correct. Here are the changes so far<br />
<br />
<center><br />
1992 5 of 45 1 of 45<br><br />
1997 5 or 49 1 of 42<br><br />
2002 5 of 55 1 of 42<br><br />
2005 5 of 55 1 of 42<br><br />
</center><br />
<br />
While the lottery officials want to have higher jackpots, they also do not want too long a period between jackpots. Normally the increase in the size of the lottery, when no one wins the jackpot, is determined by the amount taken in in this unsuccessful drawing. This was recently changed so that, when a new record jackpot occurs and no-one wins it, at most 25 million dollars are added to the Jackot until someone wins the jackpot. The money save by this is added to the second prize.<br />
<br />
When the 340 million jackpot was won, 49 players had the five basic numbers correct but not the bonus numbers. For these winners the $200,000 prize had 653,492 added to their prize so they each won $853,492. If they chosen the Powerball play option for an extra $1 their $200,000 would have been multiplied by 2,3,4, or 5 with equal probabilities. Thus if Gregg had chosen the Powerball play option, and been lucky, he would have won 1,653,492 dollars that he could add to his 15 or so million dollars he has in stocks. <br />
<br />
===DISCUSSION===<br />
<br />
(1) Do you think it is fair to advertise the lottery prize as 340 million when the cash prize is only 164.4 million?<br />
<br />
(2) What is the probability of winning the second prize?<br />
<br />
(3) Assuming that the estimate 106 million for the number of tickets sold find the expected number of second prize winners.<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Mammograms Validated as Key in Cancer Fight==<br />
<br />
The ''New York Times'' [http://www.nytimes.com/2005/10/27/health/27breast.html reported] on October 27, 2005 on a new National Cancer Institute study that attributed a significant decrease in the death rate from breast cancer to mammogram screening tests. The study, published in the New England Journal of Medicine, found that from 28% to 65% of the sharp 24% decrease in breast cancer death rates from 1990 to 2000 was due to screening; the remainder was attributed to new drugs used to treat the disease.<br />
<br />
Prior to this study, the value of mammogram screening had been disputed, for several reasons. In the general population, the test results in a large proportion number of false positives, about 90%. Thus, many women who are cancer-free are subjected to unnecessary procedures. Also, approximately 30% of cancers that are detected and treated would not have progressed significantly. Unfortunately, it isn't possible to distinguish between these so-called ''indolent'' cancers and those that become life-threatening, so it is routine practice to treat them all.<br />
<br />
The new study suggests that the benefits of routine mammography are more certain than earlier believed, according to Don Berry, Chairman of the biostatistics department of M. D. Anderson Cancer Center, in Houston, Texas, and the lead author of the paper. He said that the new study for the first time properly separates the effects of therapy and screening. Nonetheless, he cautioned that mammography does pose risks, and recommended that women be counselled before screening.<br />
<br />
Contributed by Bill Jefferys<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div></div>Nano12https://www.causeweb.org/wiki/chance/index.php?title=Chance_News_7&diff=1560Chance News 72005-11-05T09:35:11Z<p>Nano12: /* Further reading */</p>
<hr />
<div>Sept 26 2005 to Oct 15 2005<br />
==Quotation==<br />
<blockquote><br />
While writing my book [Stochastic Processes] I had an argument with Feller [Introuction to Probability Theory and its Applications]. He asserted that everyone said "random variable" and I asserted that everyone said "chance variable." We obviously had to use the same name in our books, so we decided the issue by a stochastic procedure. That is, we tossed for it and he won. </blockquote><br />
<br />
<p align = right> Joe Doob<br><br />
[http://www.dartmouth.edu/~chance/Doob/conversation.html Statistical Science]<br><br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Forsooth==<br />
<br />
Peter Winkler suggested our first forsooth.<br />
<br />
<blockquote>Texas beats Ohio State in their opening game <br />
of the season (Saturday Sept 10 2002). The sportscasters (legendary Brent Musburger on play-by-play or Gary Danielson on analysis) observed that of the 14 teams who have <br />
previously played in the championship game (at the end of each season) 5 <br />
have suffered an earlier defeat. "Thus," they conclude, "Ohio State can <br />
still make it to the championship game, but their chances are now less <br />
than 50%."</blockquote><br />
<br />
===Discussion===<br />
<br />
What is wrong with this?<br />
----<br />
Here are forsooths from the September 2005 issues of RSS NEWS<br />
<br />
<blockquote>'Big ticket quiz' at the start of Wimbledon:<br><br><br />
Q. How many punnets (a small light basket or other container for fruit or vegetables) of strawberries are eaten each day during the Wimbledon tournament?<br><br />
Is it (a) over 8,000, (b) over 9,000 or (c) over 10,000?</blockquote><br />
<br />
<div align="right">BBC radio 5<br><br />
20 June 2005</div><br />
<br />
<blockquote>Waiting time for foot surgery down by 500%</blockquote><br />
<br />
<div align="right">Evening News (Edinburgh)<br><br />
5 July 2005</div><br />
<br />
The next two forsooths are from the October RSS news.<br />
<br />
<blockquote>In 1996-8 when the number attending university was static, the participation of women was also static, but male participation fell.</blockquote><br />
<br />
<div align="right">The Times Higher<br><br />
21 January 2005</div><br />
<br />
<blockquote>[On the subject of congestion on the London Underground..] 'Last year 976 million of us used the tube...'</blockquote><br />
<br />
<div align="right">BBC London News<br><br />
19 May 2005</div><br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Fortune's Formula==<br />
<br />
''Fortune's Formula: Wanna Bet?''<br><br />
''New York Times Book Section'', September 25, 2005<br><br />
David Pogue<br />
<br />
This must be the kind of review that every Science writer dreams of. Pogue ends his review with:<br />
<br />
<blockquote> ''Fortune's Formula'' may be the world's first history book, gambling primer, mathematics text, economics manual, personal finance guide and joke book in a single volume. Poundstone comes across like the best college professor you ever had, someone who can turn almost any technical topic into an entertaining and zesty lecture. But every now and then, you can't help wishing there were some teaching assistants on hand to help.</blockquote><br />
<br />
The author William Poundstone is a science writer who has written a number of very successful science books. His book, ''Prisoner's dilemma: John von Neumann, game theory and the puzzle of the bomb'', was written in the style of this book. Indeed Helen Joyce, in her review of this book in Plus Magazine writes:<br />
<br />
<blockquote>This book is a curious mixture of biography, history and mathematics, all neatly packaged into an entertaining and enlightening read. </blockquote><br />
<br />
Poundstone describes himself as a visual artist who does books as a "day job.". You can learn about his art work [http://www.uiowa.edu/~iareview/tirweb/feature/poundstone/interview2.htm here].<br />
<br />
''Fortune's Formula'' is primarily the story of Edward Thorp, Claude Shannon, and John Kelly and their attempt to use mathematics to make money gambling in casinos and on the stock market. None of these did their graduate work in mathematics. Thorp and Kelly got their Phd's in physics and Shannon in Genetics. <br />
<br />
In the spring of 1955, while a graduate student at UCLA, Thorp joined a discussion on the possiblity of making money from roulette. Thorp suggested that they could taking advantage of the fact that bets are still accepted for a few second after the croupier releases the ball, and in these seconds, he could estimate what part of the wheel the ball would stop. <br />
<br />
Thorp did not pursue this and in 1959 became an instructor in mathematics at M.I.T. Here he became interested in blackjack and developed his famous card counting method for wining at blackjack. He decided to publish his method in the most prestigious journal he could find and settled on ''Proceedings of the National Academy of Sciences''. For this he needed to have a member of the Academy submit his paper. The only member in the math department was Shannon so he had to persuade him of the importance of his paper. Shannon not only agreed but in the process became fascinated by Thorp's idea for beating roulette. He agreed to help Thorp carry this out. They built a roulette machine in Shannon's basement. It worked fine there in trial runs but not so well in the casino so they did not pursue this method of getting rich. <br />
<br />
Of course Thorp is best known for showing that blackjack is a favorable game and giving a method to exploit this fact. Shannon is best known for his work in information theory. Kelly is known his method for gambling in a favorable game. This plays a central role in Poundstone's book and is probably why Pogue felt that it would help if he had a teaching assistant. Poundstone tries to explain Kelly's work in many different ways but what he really needed to understand it is an example but this required too many formulas for a popular book. So we shall include an example from Chance News 7.09. <br />
<br />
Writing for Motley Fool, 3 April 1997 Mark Brady complained about the inumeracy of the general public and gave a number of examples including this one:<br />
<br />
<blockquote> Fear of uncertainty and innumeracy are synergistic. Most people cannot do the odds. What is a better deal over a year? A 100% safe return with 5 percent interest or a 90 percent safe return with a 20 percent return. For the first deal, your return will be 5% percent. For the second, your return will be 8%. Say you invest $1000 10 times. Your interest for the 9 successful deals will be 9000 x 0.2 or 1800. Subtract the 1000 you lost on the 10th deal and you get a $800 return on your original $10,000 for 8 percent.</blockquote><br />
<br />
Peter Doyle suggested that a better investment strategy in this case is:<br />
<br />
Faced with a 100 percent-safe investment returning 5 percent and a 90 percent-safe investment returning 20%, you should invest 20% of your funds in the risky investment and 80% in the safe investment. This gives you an effective return of roughly 5.31962607969968292 percent. <br />
<br />
Peter is using a money management system due to J. L. Kelly (1956: "A new interpretation of information rate," ''Bell System Technical Journal'', '''35'''). Kelly was interested in finding a rational way to invest your money faced with one or more investment schemes, each of which has a positive expected gain. He did not think it reasonable to try simply to maximize your expected return. If you did this in the Motley Fools example as suggested by Mark Brady, you would choose the risky investment and might well lose all your money the first year. We will illustrate what Kelly did propose in terms of Motley Fools example. <br />
<br />
We start with an initial capital, which we choose for convenience to be $1, and invest a fraction r of this money in the gamble and a fraction 1-r in the sure-thing. Then for the next year we use the same fractions to invest the money that resulted from the first year's investments and continue, using the same r each year. Assume, for example, that in the first and third years we win the gamble and in the second year we lose it. Then after 3 years our investment returns an amount f(r) where: <br />
<br />
<math><br />
f(r) = (1.2r + 1.05(1-r))(1.05(1-r))(1.2r + 1.05(1-r)). <br />
</math><br />
<br />
After n years, we would have n such factors, each corresponding to a win or a loss of our risky investment. Since the order of the terms does not matter our capital will be: <br />
<br />
<math><br />
f(r,n) = (1.2r + 1.05(1-r))^W(1.05(1-r))^L<br />
</math><br />
<br />
where W is the number of times we won the risky investment and L the number of times we lost it. Now Kelly calls the quantity:<br />
<br />
<math><br />
G(r) =\lim_{n \to \infty }\frac{\log(f( r,n)} {n}<br />
</math> <br />
<br />
the exponential rate of growth of our capital. In terms of G(r) our capital should grow like <math> e^{G(r)} </math>. In our example: <br />
<br />
<math><br />
\log(\frac{f(r,n)}{n}) = \frac{W}{n}\log(1.2r + 1.05(1-r)) + \frac{L}{n}\log(1.05(1-r))<br />
</math> <br />
<br />
Since we have a 90% chance of winning our gamble, the [http://en.wikipedia.org/wiki/Strong_law_of_large_numbers#The_strong_law strong law of large numbers] tells us that as n tends to infinity this will converge to <br />
<br />
<math><br />
G(r) = 0.9\log(1.2r + 1.05(1-r))+0.1\log(1.05(1-r))<br />
</math><br />
<br />
It is a simple calculus problem to show that G(r) is maximized by r = 0.2 with: <br />
G(0.2) = 0.05183. Then e^{0.05183} = 1.0532, showing that our maximum rate of growth is 5.32% as claimed by Peter. <br />
<br />
The attractiveness of the Kelly investment scheme is that, in the long run, any other investment strategy (including those where you are allowed to change your investment proportions at different times) will do less well. "In the long run and less well" means more precisely that the ratio of your return under the Kelly scheme and your return under any other strategy will tend to infinity.<br />
<br />
Thorp had a very good experience in the stock market, which is described very well by Gaeton Lion in his excellent [http://www.amazon.com/gp/product/customer-reviews/0809046377/ref=cm_cr_dp_pt/103-8647004-5865443?%5Fencoding=UTF8&n=283155&s=books review] of ''Fortune's Formula''. He writes:<br />
<br />
<blockquote> Ed Thorp succeeded in deriving superior returns in both gambling and investing. But, it was not so much because of Kelly's formula. He developed other tools to achieve superior returns. In gambling, Ed Thorp succeeded at Black Jack by developing the card counting method. He just used intuitively Kelly's formula to increase his bets whenever the odds were in his favor. Later, he ran a hedge fund for 20 years until the late 80s and earned a rate of return of 14% handily beating the market's 8% during the period. <br><br><br />
<br />
Also, his hedge fund hardly lost any value on black Monday in October 1987, when the market crashed by 22%. The volatility of his returns was far lower than the market. He did this by exploiting market inefficiencies using warrants, options, and convertible bonds. The Kelly formula was for him a risk management discipline and not a direct source of excess return. </blockquote><br />
<br />
Shannon also made a lot of money on the stock market, but did not use Kelly's formula. In his [http://www.amazon.com/gp/product/customer-reviews/0809046377/ref=cm_cr_dp_pt/103-8647004-5865443?%5Fencoding=UTF8&n=283155&s=books review] Gaeton Lion writes<br />
<br />
<blockquote>Claude Shannon amassed large wealth by recording one of the best investment records. His performance had little to do with Kelly's formula. Between 1966 and 1986, his record beat even Warren Buffet (28% to 27% respectively). Shannon strategy was similar to Buffet. Both their stock portfolios were concentrated, and held for the long term. Shannon achieved his record by holding mainly three stocks (Teledyne, Motorola, and HP). The difference between the two was that Shannon invested in technology because he understood it well, while Buffet did not. </blockquote><br />
<br />
Finally, Thorp provided the following comments for the book cover:<br />
<br />
<blockquote>From bookies to billionaires, you'll meet a motley cast of characters in this highly original, 'outside the box' look at gambling and investing. Read it for the stories alone, and you'll be surprised at how much else you can learn without even trying. --Edward O. Thorp, author of ''Beat the Dealer'' and ''Beat the Market''.</blockquote><br />
<br />
Submitted by Laurie Snell.<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Which foods prevent cancer?==<br />
<br />
Which of these foods will stop cancer? (Not so fast)<br><br />
New York Times, 27 September 2005, Sect. F, p. 1<Br><br />
Gina Kolata<br />
<br />
Among other examples, the article includes a [http://www.nytimes.com/imagepages/2005/09/26/science/20050927_CANCER_GRAPHIC.html data graphic] on purported benefits of dietary fiber in preventing colorectal cancer. Early observational studies indicated an association, but subsequent randomized experiments found no effect. <br />
<br />
More to follow.<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Slices of risk and the <em>broken heart</em> concept==<br />
[http://www.gloriamundi.org/picsresources/news20050912.pdf How a Formula Ignited Market That Burned Some Big Investors],<br />
Mark Whitehouse, The Wall Street Journal, September 12, 2005.<br><br />
<br />
This on-line article relates how a statistician, David Li,<br />
unknown outside a small coterie of finance theorists, helped change the world of investing. <br />
<br />
The article focuses on a event last May when General Motors Corp's debt<br />
was downgraded to junk status, causing turmoil in some financial markets.<br />
The article gives a nice summary of the underlying financial instruments known<br />
as credit derivatives -<br />
investment contracts structured so their value depends on the behavior of some other thing or event -<br />
with exotic names like <br />
[http://en.wikipedia.org/wiki/Collateralized_debt_obligations collateralized debt obligations] and [http://en.wikipedia.org/wiki/Credit_default_swap credit-default swaps].<br />
<br />
The critical step is to estimate the likelihood that many of the companies <br />
in a pool of companies would go bust at once. <br />
For instance, if the companies were all in closely related industries,<br />
such as auto-parts suppliers, they might fall like dominoes after a catastrophic event.<br />
Such a pool would have a 'high default correlation'.<br />
<br />
In 1997, nobody knew how to calculate default correlations with any precision. <br />
Mr. Li's solution drew inspiration from a concept in actuarial science known as the <br />
<em>broken heart</em> syndrome - people tend to die faster after the death of a beloved spouse. <br />
Some of his colleagues from academia were working on a way to predict this<br />
death correlation, something quite useful to companies that sell life insurance and joint annuities.<br />
He says:<br />
<blockquote><br />
Suddenly I thought that the problem I was trying to solve was exactly like the problem these<br />
guys were trying to solve,.<br />
Default is like the death of a company, so we should<br />
model this the same way we model human life."<br />
</blockquote><br />
<br />
This gave him the idea of using [http://en.wikipedia.org/wiki/Copula_%28statistics%29 copulas], <br />
mathematical functions the colleagues had begun applying to actuarial science. <br />
Copulas help predict the likelihood of various events<br />
occurring when those events depend to some extent on one another. <br />
Until the events last May of this year, one of the most popular copulas for bond pools <br />
was the Gaussian copula, named after <br />
[http://en.wikipedia.org/wiki/Carl_Friedrich_Gauss Carl Friedrich Gauss], a 19th-century German statistician. <br />
<br />
===Further reading===<br />
* The [http://www.gloriamundi.org/picsresources/news20050912.pdf on-line article] gives more details about what went wrong in the financial markets in May and the search for a more appropriate copula to capture better the <em>broken heart</em> syndrome between companies.<br />
* [http://en.wikipedia.org/wiki/Wikipedia Wikipedia] is a very worthwhile on-line resource for definitions of technical words, such as [http://en.wikipedia.org/wiki/Copula_%28statistics%29 copula].<br />
<br />
Submitted by John Gavin.<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Learning to speak via statistics and graph theory==<br />
<br />
[http://education.guardian.co.uk/tefl/teaching/story/0,15085,1576100,00.html Computer learns grammar by crunching sentences], Max de Lotbinière September 23, 2005, [http://www.guardianweekly.co.uk/ Guardian Weekly].<br><br />
[http://www.cornellsun.com/vnews/display.v/ART/2005/09/09/432118a84f6af Profs’ New Software ‘Learns’ Languages], Ben Birnbaum, 9 Sep 2005, Cornell Daily Sun.<br />
<br />
A language-learning robot may sound like science fiction but new software, developed by Cornell University psychology professor Shimon Edelman, with colleagues Zach Solan, David Horn and Eytan Ruppin from Tel Aviv University in Israel, is well on the way to constructing a computer program that can teach itself languages and make up its own sentences, the developers' claim.<br />
<br />
Unlike previous attempts at developing computer algorithms for language learning - "Automatic Distillation of Structure," or "ADIOS" for short - discovers complex patterns in raw text by repeatedly aligning sentences and looking for overlapping parts.<br />
Once it has derived a language's rules of grammar,<br />
it can then produce sentences of its own, simply from blocks of text in that language.<br />
<br />
It has been evaluated on artificial context-free grammars with thousands of rules, <br />
on natural languages as diverse as English and Chinese, <br />
on coding regions in DNA sequences and on protein data correlating sequence with function. <br />
<br />
Edelman comments:<br />
<blockquote><br />
Adios relies on a statistical method for pattern extraction and on structured generalisations <br />
- the two processes that have been implicated in language acquisition.<br />
Our experiments show that Adios can acquire intricate structures <br />
from raw data including transcripts of parents' speech directed at two- or three-year-olds.<br />
This may eventually help researchers understand how children, <br />
who learn language in a similar item-by-item fashion, and with little supervision, <br />
eventually master the full complexity of their native tongue.<br />
</blockquote><br />
<br />
[http://plus.maths.org/latestnews/may-aug05/adios/ Plus Magazine's website]<br />
offers a more logical explanation:<br />
<blockquote><br />
The ADIOS algorithm is based on statistical and algebraic methods performed on one of the most basic and versatile objects of mathematics - the graph.<br />
Given a text, the program loads it as a graph by representing each word by a node, or vertex, and each sentence by a sequence of nodes connected by lines. A string of words in the text is now represented by a path in the graph. <br><br />
<br />
Next it performs a statistical analysis to see which paths, or strings of words, occur unusually often. <br />
It then decides that those that appear most frequently - called "significant patterns" - <br />
can safely be regarded as a single unit<br />
and replaces the set of vertices in each of these patterns by a single vertex, <br />
thus creating a new, generalised, graph.<br><br />
<br />
Finally, the program looks for paths in the graph which just differ by one vertex. <br />
These stand for parts of sentences that just differ by one word (or compound of words) like "the cat is hungry" and "the dog is hungry". <br />
Performing another statistical test on the frequency of these paths, the program identifies classes of vertices, or words, that can be regarded as interchangeable, or equivalent. <br />
The sentence involved is legitimate no matter which of the words in the class - in our example "cat" or "dog" - you put in.<br><br />
<br />
This last step is then repeated recursively.<br><br />
</blockquote><br />
<br />
[http://plus.maths.org/latestnews/may-aug05/adios/ The website] uses graphs to illustrate some examples and it finishes with some reassuring words:<br />
<blockquote><br />
All this doesn't mean, of course, that the program actually "understands" what it's saying. It simply knows how to have a good go at piecing together fragments of sentences it has identified, in the hope that they are grammatically correct. So if, like me, you're prone to swearing at your computer, you can safely continue to do so: it won't answer back for a long while yet.<br />
</blockquote><br />
<br />
===Further reading===<br />
The [http://adios.tau.ac.il/ ADIOS homepage] offers an overview and more detailed description of the program.<br />
<br />
Submitted by John Gavin.<br />
<br />
==Understanding probability==<br />
<br />
Understanding Probability:Chance rules in everyday life<br><br />
Cambridge University Press 2004<br><br />
Henk Tijms<br />
<br />
Hank Tijms is Professor in Operation Research at the Vrije University in Amsterdam. This book is based on his earlier Dutch book “Spelen met Kansen.” <br />
<br />
The aim of this book is to show how probability applies to our everyday life in a way that your Uncle George could understand even if he has forgotten much of his high school math. Tijms does not try to avoid mathematics but only to postpone the formal math until the reader has seen the many applications of probability in the real world, how much fun it is, and learned to work problems and when he can’t work one how to get the answer by simulation. He learns all this in part I of the book and then he learns the more formal math in Part II.<br />
<br />
In Chapter 1 Tijms asks the reader to think about problems with surprising answers in the spirit of Susan Holmes “[http://www-stat.stanford.edu/~susan/surprise/ Probability by Surprise]” including the birthday problem and the Monty Hall problem. Readers are on their own to try to solve one or more of the problems but promised that they will see the solutions later in the book. <br />
<br />
Chapter 2 deals with the law of large numbers and introduces the concept of simulation. This theorem is explained and illustrated by problems related, for example, to coin tossing, random walks and casino games. Expected value is introduced in an informal way to be defined more carefully later in the book. For the reader who is not frightened by mathematical formulas, Tijms includes a discussion of the Kelly betting system with a footnote saying that this paragraph can be skipped at first reading. This is a fascinating topic that is widely applied in gambling and stock investment but rarely appears in a probability book.<br />
<br />
In Chapter 3 the author returns to previous problems such as the birthday problem and gambling systems and solves them first by simulation and then by mathematics. <br />
<br />
In this chapter Tijms describes Efron’s bootstrap method and uses it to solve a number of problems including a hypothetical clinical trial and to test if the famous 1970 draft lottery during the Vietnam War was fair. Again the bootstrap method has wide application but rarely occurs in an elementary probability or statistics book.<br />
<br />
Chapter 4 describes the binomial, Poisson, and hypergeomtric distributions and how to use them in solving problems such as the famous hat check problem, and a variety of interesting lottery questions. The Poisson process is discussed but again with the footnote that novice readers might want to read this at a later time.<br />
<br />
Chapter 5 is mainly about Center Limit Theorem and its many applications especially to statistics. <br />
<br />
Chapter 6 introduces Chance trees and Bayes’s rule. The tree method is used to explain a variety of problems including the Monty Hall Problem and the false-positive paradox. <br />
<br />
This is a brief description of the first six chapters which constitute Part I of the book. Now the fun is over. Part 2 called “Essentials of probability” looks like the traditional first chapters in a standard probability book. But the reader has already found how exciting probability is, has a good intuitive idea of the basic concepts and has worked many of the interesting problems at the end of each chapter either using math or simulation. For some students this might allow them to actually enjoy Part 2. But your Uncle George may want to quit while they are ahead. <br />
<br />
Tijms writes with great clarity and his enthusiasm for probability in the real world is contagious. We were delighted to see, as acknowledged in the preface, that Tijms included several of the more interesting problems discussed in Chance News, often going well beyond what we had said in our discussion of the problem. <br />
<br />
This book presents a completely new way to go about teaching a first course in probability and we think those who teach such a course should consider trying it out.<br />
<br />
===Discussion===<br />
<br />
(1) In the days of Basic we required all students to learn Basic in their first math course so we could assume that students could write programs to simulate probability problems and so me made heavy use of simulation as suggested in this book. The author uses Pascal in his book. What present language do you think is easiest for a student with no computing experience to learn?<br />
<br />
We asked Professor Tijms what the situation was in math departments in Europe and he replied:<br />
<br />
<blockquote>In math departments of universities and polytechnic schools in Europe students learn to write computer programs. In my university they still learn to program in Java and C++ ( in previous days Pascal), but I see in the Netherlands the trend that the instructors think it is sufficient if the students are able to program in Matlab. <br><br><br />
<br />
In ny book I have chosen to formulate the simulation programs in Pascal because of the clarity and the simplicity of the language, though this language is hardly used anymore. The introductory probability course at my university is given before they have learned to program, but this does not prevent them of simulating probability problems by using Excel. In the simulation of many elementary probability problems a random-number generator alone suffices to simulate those problems and so Excel can be used. In the second year they have mastered Matlab, a perfect tool with its excellent graphics to simulate many challenging probability problems ( they really like it, in particular when it concerns problems such as the problems 2.24-2.45 in chapter 2 and the problems 5.11-5.13 in chapter 5). <br />
</blockquote><br />
<br />
<br />
(2) Do you think that probability books should include data to test probability models that are said to describe real world problems? If so name some models that you think would pass such a test and some that you think might not.<br />
<br />
Submitted by Laurie Snell<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Societies worse off when they have God on their side==<br />
<br />
[http://www.timesonline.co.uk/article/0,,2-1798944,00.html Societies worse off when they have God on their side]<br><br />
Timesonline, September 27, 2005<br><br />
Ruth Gledhill<br />
<br />
[http://moses.creighton.edu/JRS/2005/2005-11.html Cross-national correlations of quantifiable societal health with popular religiosity and secularism in the prosperous democracies]<br><br />
Journal of Religion & Society, Vol.7(2005)<br><br />
Gregory S. Paul<br />
<br />
In the Times article we read:<br />
<br />
<blockquote>According to the study, belief in and worship of God are not only unnecessary for a healthy society but may actually contribute to social problems.<br><br><br />
Many liberal Christians and believers of other faiths hold that religious belief is socially beneficial, believing that it helps to lower rates of violent crime, murder, suicide, sexual promiscuity and abortion. The benefits of religious belief to a society have been described as its “spiritual capital”. But the study claims that the devotion of many in the US may actually contribute to its ills. <br />
</blockquote><br />
<br />
Gregory Paul is a dinosaur paleontologist and on an [http://www.abc.net.au/worldtoday/indexes/2005/twt_20050928.htm interview] on Australian ABC radio Paul said that, being a paleontologist, for many years he had to deal with the issue of creationism versus evolutionary science in the U.S and his interest in evolutionary science prompted him to look at whether there was any link between the religiosity of a society and how well that society functions. <br />
<br />
If you look at Paul's article you will find very little technical statistical analysis, for example, he did not carry out a regression analysis. Rather he rests his case on the series of scatterplots.<br />
<br />
Paul describes his data sources as:<br />
<br />
<blockquote>Data sources for rates of religious belief and practice as well as acceptance of evolution are the 1993 Environment I (Bishop) and 1998 Religion II polls conducted by the International Social Survey Program (ISSP), a cross-national collaboration on social science surveys using standard methodologies that currently involves 38 nations. The last survey interviewed approximately 23,000 people in almost all (17) of the developed democracies; Portugal is also plotted as an example of a second world European democracy. Results for western and eastern Germany are combined following the regions' populations. England is generally Great Britain excluding Northern Ireland; Holland is all of the Netherlands. The results largely agree with national surveys on the same subjects; for example, both ISSP and Gallup indicate that absolute plus less certain believers in a higher power are about 90% of the U.S. population. The plots include Bible literalism and frequency of prayer and service attendance, as well as absolute belief in a creator, in order to examine religiosity in terms of ardency, conservatism, and activities. </blockquote><br />
<br />
Here are the countries Paul considered with the abbreviations used on the graphics. <br />
<br />
A = Australia, C = Canada, D = Denmark, E = Great Britain, F = France, G = Germany,<br />
H = Holland, I = Ireland, J = Japan, L = Switzerland, N = Norway, P = Portugal, R = Austria,<br />
S = Spain, T = Italy, U = United States, W = Sweden, Z = New Zealand.<br />
<br />
There seems to be no agreement as to which countries are developed democracies. For example Paul might have included Greece and Belgium, Finland, and others but the data may have determined his choice. Paul comments that he added Portugal as an example of a second world democracy. <br />
<br />
Paul's anaysis of the data includes a series of 9 Figures which are available at the end of the article and are the most interesting part of the study. If you try printing Paul's article you will only get the first of his 9 Figures. When you look at the [http://moses.creighton.edu/JRS/2005/2005-11.html web version] you will still see only Figure 1 but the others can be viewed by selecting the numbers from 2 to 9 on the left side of Figure 1.<br />
<br />
Figure 1 deals with the proportion of people who accept human evolution which is interesting but not as relevant to the welfare of the people as others so we will look at Figure 2.<br />
<br />
[[Image:religion2.png|500px|center|Source:Gregory Paul]]<br />
<br />
Each Figure iprovides 5 separate scatterplots. Ïn Figure 2 we see that the U.S. has largest number--between 6 and 7-- of homicides per 100,000 and Spain has the lowest number with less than 1 homicide per 100,000. We also see that the U.S. has the highest proportion of people, about 25%, who take the bible literally while several countries have less than 10% such people.<br />
<br />
What we cannot do is compare the number of homicides per thousand between those who take the bible literally and those who are agnostics or atheists which is what we would really want to know. Presumably the data did not permit this comparison. <br />
<br />
[[Image:religion3.png|500px|center|Source:Gregory Paul]]<br />
<br />
Figure 3 deals with "14-24 year old suicides per 100,000". Here the U.S. is in about the middle.<br />
<br />
Figure 4 deals with the "under-five mortalities per 1000 births".<br />
<br />
[[Image:religion4.png|500px|center|Source:Gregory Paul]]<br />
<br />
Ignoring Portugal, the U.S. has the highest number of under-five mortalities per 1000 births-- between 7 and--8 while several countries have only 4.<br />
<br />
The other figures can be seen at end of Paul's article. They deal with life expectancy, sexually transmitted diseases, abortion and 15-16 year old pregnancies. Life expectancy is the smallest in the U.S. and for sexually transmitted diseases, abortion and 15-17 year old prenacies the U.S. is at the top of the graphs and in fact these look like outliers.<br />
<br />
Well, this study does not by itself justify the Times hedline: "Societies worse off when they have God on their side." Paul himself would not claim this. He writes:<br />
<br />
<blockquote> This study is a first, brief look at an important subject that has been almost entirely neglected by social scientists. The primary intent is to present basic correlations of the elemental data. Some conclusions that can be gleaned from the plots are outlined. This is not an attempt to present a definitive study that establishes cause versus effect between religiosity, secularism and societal health. It is hoped that these original correlations and results will spark future research and debate on the issue.</block<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div></div>Nano12https://www.causeweb.org/wiki/chance/index.php?title=Chance_News_9&diff=1565Chance News 92005-11-05T09:35:08Z<p>Nano12: /* item2 */</p>
<hr />
<div>==Quotation==<br />
Å quotation will be added here.<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Forsooth==<br />
Forsooth items should be added here.<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Supreme Court Nominee Alito: Statistics Misleading?==<br />
An [http://www.salon.com/politics/war_room/2005/10/31/jury/index.html article] in Salon.com for October 31 discusses the first-degree murder trial, Riley v. Taylor. The defendant Riley was African-American; at the trial, the prosecution used its peremptory challenges to eliminate all three of the African-Americans on the jury panel. In the same county that year, there were three other first-degree murder trials, and in every one of those cases all of the African-American jurors were struck.<br />
<br />
A majority of the judges on the appeals court thought that there was evidence that jurors were struck for racial reasons. According to them, a simple calculation indicates that there should have been five African-American jurors amongst the forty-eight that were empanelled. However, there were none. To these judges, this was clear evidence of racial motivaion in the striking of such jurors.<br />
<br />
Judge Alito dissented. He called the majority's analysis simplistic, and stated that although only 10% of the U.S. population is left-handed, five of the last six people elected president of the United States were left-handed. He asked rhetorically whether this indicated bias against right-handers amongst the U.S. electorate.<br />
<br />
The majority responded that there is no provision in the Constitution that protects persons from discrimination based on whether they are right-handed or left-handed, and that to compare these cases with the handedness of presidents ignores the history of racial discrimination in the United States.<br />
<br />
===Questions===<br />
<br />
1) Assuming that Judge Alito is correct about the proportion of left-handers in the U.S. population, what is the probability that five of the last six presidents elected would be left-handed?<br />
<br />
2) Is Judge Alito's comparison biased by the fact that he chose just the last six presidents? Presumably he believed that the president just before this group was right-handed, otherwise he would have included him in the sample and said "six of the last seven presidents." What is the relevant statistic?<br />
<br />
3) When the decision came down in 2001, the last six people elected president were George W. Bush, Clinton, George H. W. Bush, Reagan, Carter and Nixon. Of these, Clinton and George H. W. Bush were left-handed. Ford, who was left-handed, was not elected president (or even vice-president); he became president upon the resignation of Richard Nixon. Reagan may have been left-handed as a child, but he wrote right-handed so his case isn't clear; the Reagan Presidential Library [http://www.reagan.utexas.edu/archives/reference/facts.html says] that he was "generally right-handed." Judge Alito may have been confused, including on his list Ford (who was not elected) and George W. Bush (who is not left-handed, although his father is), as well as Reagan. The other left-handed presidents were Truman and Garfield. Hoover is found on some lists of left-handed presidents, but according to the Hoover Institution, he was not left-handed. How does this information affect Alito's argument?<br />
<br />
4) Suppose that 5/48 of the jury pool were African-American. What is the probability that no juror amongst the 48 selected would have been African-American? How does this compare with the actual statistics of left-handed presidents? Does the same objection apply to this case as might apply to Alito's example?<br />
<br />
5) What is your opinion? Is there clear statistical evidence of racial bias in the use of peremptory challenges in this county?<br />
<br />
6) What does it say about our judiciary that Judge Alito could get his facts as wrong as he did, and that none of the judges in the majority caught the errors?<br />
<br />
Contributed by Bill Jefferys<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==item2==<br />
Replace item2 by the name of your article.<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div></div>Nano12https://www.causeweb.org/wiki/chance/index.php?title=Chance_News_8&diff=1559Chance News 82005-11-05T09:35:05Z<p>Nano12: /* A record powerball lottery jackpot */</p>
<hr />
<div>Oct 15 to Oct 30<br />
<br />
==Quotation==<br />
<blockquote>One more fagot of these adamantine bandages, is, the new science of Statistics. It is a rule, that the most casual and extraordinary events -- if the basis of population is broad enough -- become matter of fixed calculation. It would not be safe to say when a captain like Bonaparte, a singer like Jenny Lind, or a navigator like Bowditch, would be born in Boston: but, on a population of twenty or two hundred millions, something like accuracy may be had. Ralph Waldo Emerson Fate</blockquote><br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Forsooth==<br />
Here's another Forsooth from the October issue of RSS News.<br />
<blockquote>Your'e more likely to die in a fire in Strathclyde than anywhere else in the country</blockquote><br />
<br />
<div align="right">BBC1 mews bullietin<br><br />
11 May 2005</div><br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==The Poisson distribution and the Supreme Court==<br />
The Poisson distribution and the Supreme Court<br><br />
''Journal of the American Statistical Association'' 31, no. 195 ,(1936), 376-80<br><br />
W. Allen Wallis<br />
<br />
Supreme Court Appointments as a Poisson distribution<br><br />
''American Journal of Political Science'', 26, No.1, February 1982<br><br />
S. Sidney Ulmer<br />
<br />
This is not current news, but since Supreme Court appointments are in the news we felt that these articles might make an interesting class discussion.<br />
<br />
In 1936 statistician Allen Wallis suggested that a Poisson distribution can approximate the number of U.S. Supreme Court appointments in a given year. In his Table 1 Wallis provided the number appointed in each year over the intervals with different numbers of Justices on the Supreme Court: 1790-1806 (6) 1807-1836 (7), and 1837-1932 (9). Actually there were 10 in the years 1963 to 1967 which Wallis called "negligible exceptions."<br />
<br />
[[Image:wallis1.png|500px|center]]<br />
<br />
Wallis then restricts himself to the years 1837-1932 and finds that a Poisson distribution with mean .5 can approximate the number of court appointments in a year. His results are shown in his Figure II:<br />
<br />
[[Image:wallis2.png|500px|center]]<br />
<br />
In his article, Sidney Ulmer updated the data to 1980 and also includes data from the early Supreme Courts with 6 and 7 members. Thus his data covers the years 1790--1980. His Table 1 compares the actual number of appointments in a year with the expected number of appointments assuming a Poisson distribution with mean 5.13.<br />
<br />
[[Image:ulmer1.png|500px|center]]<br />
<br />
In his Table II Ulmer limits the data to the 9 member Supreme Courts: 1837 to 1862 and 1869-1980).<br />
<br />
[[Image:ulmer2.png|500px|center]]<br />
<br />
Testing the goodness of fits, Ulmer argues that the fit with the varying size Supreme Courts is just as good as with fixed size Supreme Courts.<br />
<br />
===DISCUSSION===<br />
<br />
(1) What is the probability that a President will make 2 or more appointments to the Supreme Court during a 4-year term? What is the probability a President makes no appointments during a 4-year term? Has this ever happened?<br />
<br />
(2) Do you agree with Ulmer that there is no reason to limit the data to years with the Supreme Court is the same size?<br />
<br />
(3) Obtain the data needed to update Ulmer's results to today and provide Tables that correspond to Ulmer's Tables 1 and 2. Add your Tables to this Chance News and make your data available to make it easier to update this in future years.<br />
<br />
Contributed by Laurie Snell<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Possible Cancer Cluster in Connecticut==<br />
Pratt Agrees to Increase Funding for Brain Cancer Study <br><br />
''The Associated Press''<br><br />
October 11, 2005<br><br />
Stephen Singer<br><br />
<br />
<br />
In a case that seems eerily familiar to the leukemia cancer cluster made famous by the book and movie, ''A Civil Action'', researchers are trying to determine whether or not a cancer cluster exists among workers at Pratt & Whitney, a company that manufactures jet engines. Over one hundred former or current Pratt & Whitney employees have been identified as having a relatively rare type of fatal brain tumor known as glioblastoma multiforme, which strikes 3 people per 100,000 every year. Many of these workers have been exposed to metals and chemical substances, including TCE (trichloroethylene), which is an engine degreaser. TCE is the same carcinogenic chemical that was dumped in the 1960’s and 1970’s by the chemical company, WR Grace, in Woburn, MA, and that was found to have contaminated the drinking water in two of the town’s wells. <br><br />
<br />
<br />
Prior to the recent announcement that the funding is being increased from $6 million dollars to $12 million dollars, this medical study was already being described as the largest occupational health study ever conducted. It covers 250,000 people who worked at any of the seven Connecticut Pratt & Whitney plants from 1952 to 2001. So far, at least 125 cases of brain cancer have been documented, according to the lawyer who represents dozens of individuals and family members.<br><br />
<br />
<br />
The study falls under the auspices of the Connecticut Department of Public Health. However, due to the overwhelming cost and scope of the study, Pratt & Whitney is funding the project. Since Pratt is paying for the study, they chose the researchers, a team from the University of Pittsburgh. The project began three years ago, and the results are expected to be available between 2007 and 2009.<br><br />
<br />
<br />
In the meantime, this case faces many of the obstacles common in the quest to establish whether or not a cancer cluster exists, such as proving causation, the fact that it can take a long time (sometimes 5-40 years) after exposure for true problems to show up, and finding the people who were exposed & convincing them to participate in the study. Additionally, there are legal difficulties for the families involved, including Connecticut’s statute of limitations laws, the length of time it takes investigators to reach a conclusion, the cost of litigation, and the “deep pockets” of a company like Pratt & Whitney.<br><br />
<br />
<br />
This case study provides a current example of an ongoing investigation into a possible cancer cluster. Will it ultimately be found to be a coincidence cluster or proven to be a true cancer cluster? Does it make sense that the researchers are including in the study everyone who worked at Pratt over a fifty year period, even those who only worked there for a brief time period and those who were not directly exposed to toxic substances (i.e. office workers)? Could the researchers possibly have an unconscious bias in favor of the company that is funding their research? If the company doesn’t fund the research, then who should? Is there some other way to structure such investigations, so that the company involved pays for the study, but is not allowed to choose the researchers and directly fund them?<br><br />
<br />
<br />
'''Further Reading'''<br><br />
<br />
• “Rare Cancer Found in Workers”, ''The New York Times'', March 10, 2002, Jane Gordon<br><br />
• “Scientist: Pratt Commits to Cancer Study”, ''The Hartford Courant'', May 19, 2005<br><br />
• “Participation in Cancer Study at Pratt Lagging”, ''The Hartford Courant'', October 12, 2005, Paul Marks<br><br />
• ''The New Haven Advocate'' has had more than a dozen articles that explain the working conditions at Pratt & Whitney, and also chronicle the history & progression of this case. These articles have been investigated and written primarily by Carole Bass, Associate Editor. A few of the articles are listed below. <br> <br />
-“Worked to Death”, August 2, 2001, Carole Bass & Camille Jackson<br><br />
-“Talking Cure”, October 28, 2004, Dave Goldberg<br><br />
-“Time’s Not on Their Side”, January 20, 2005, Carole Bass<br><br />
-“The Brains Behind the Brain”, October 20, 2005, Carole Bass <br><br />
For the early New Haven Advocate articles (i.e., 2001-2002) on this subject, go to http://old.newhavenadvocate.com/workedtodeath/index.html<br> <br />
For the articles since 2002, go to <br><br />
http://www.newhavenadvocate.com and search for Pratt & Whitney.<br><br />
<br />
Submitted by Josephine Rodriguez.<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==A record powerball lottery jackpot==<br />
<br />
On Saturday Oct 22, 2005 the powerball lottery had a record powerball jackpot of 340 million dollars. <br />
<br />
When you buy a ticket for this lottery, you specify five distinct numbers from 1 to 55, which we call basic numbers and one number from 1 to 42 called the bonus number. To win the Jackpot your 5 basic numbers and your bonus number must agree with a random choice of 5 basic numbers and one bonus number chosen by the lottery officials. The number of possible tickets is:<br />
<br />
<center><math>{55 \choose 5} 42 = </math> 146,107,962</center><br />
<br />
Thus if you buy a single ticket, the probability of having a winning jackpot ticket is<br />
<br />
<center> <math>{1} \over {146107962}</math> = .000000006844...</center><br />
<br />
The powerball website and the media expresses this by saying that the odds that you have a winning jackpot ticket is 1 in 146,107,962. <br />
<br />
Whenever there is a record jackpot, the news writers look for suggestions for other rare events that might be more familiar to its readers. <br />
<br />
Our own favorite was suggested by Fred Hoppe: if you toss a coin 27 times your chance of getting 27 heads in a row is greater than your chance of having a winning jackpot ticket when you buy a single ticket. (<math> 2^{27} = 134217728</math> and so there are 134,217,728 possible sequences of heads and tails and only 1 has all heads.)<br />
<br />
In an article for the ''Omaha World-Herald'' Oct 18, 2005 , Robynn Tysver writes:<br />
<br />
<blockquote> You have a greater chance of getting killed by lightning than winning this week's 340 million Powerball jackpot. You also have a greater chance of drowning in a bathtub. The lifetime odds of getting killed by lightning are one in 56,439, and the lifetime odds of dying while in or falling into a bathtub are one in 10,582, according to the National Safety Council. <br />
</blockquote><br />
<br />
These are not even in the ballpark. The ''Minneapolis Star Tribune'' consulted mathematicians David Bressoud and Douglas Arnold who contributed the following:<br />
<br />
According to Arnold you have a seven times better chance of becoming a saint. And Bressoud notes that you're six times more likely to get elected president of the United States. But they also provide the following more interesting estimates:<br />
<br />
<blockquote>Bressoud: "If you buy 10 tickets a week, every week, it would take you 280,000 years before you could expect to win."<br><br><br />
<br />
Arnold: "If you were to select a group of Powerball numbers every minute for 138 years, you would have about a 50 percent chance of picking the winning Powerball ticket." <br><br><br />
<br />
It is not clear what Bressoud means by "expect to win". We can check this by a simple calculation (simple for Mathematica). Let q(n) be the probability that you if you buy n tickets you fail to get a winning jackpot ticket . Then:<br />
<br />
<center> <math> \left(\frac{146107961}{146107962}\right) ^n = q(n) </math></center><br />
<br />
The average number of weeks in a year is 52.177457 so If you buy 10 tickets a week, every week for 280,000 years you will buy about 146,097,000 tickets. Using this number for n in our formula we find that you have about a 37% chance of not getting a winning lottery ticket or a 63% chance of getting one. We would not "expect to win" with a 63% chance of winning but others may. Using our formula for q(n) we find that if we buy 10 tickets a week, every week for 830,000 years you will have about a 95% chance of getting at least one winning lottery ticket which seems to us more appropriate for expecting to win. <br />
<br />
Consider now Arnold's example. Our colleague Dana Williams found that you need to buy a ticket for about 101 million lottery offerings to have about a 50% chance of getting at least one winning lottery ticket. There are an average of 525,946.766 minutes in a year. Dividing 101 million by this number gives 192.035. Thus Arnold's 138 years should be 192 years.<br />
<br />
We asked Professor Arnold about this and he replied:<br />
<br />
<blockquote> That number, which was quoted in the ''Star Tribune'' was an off-the-top-of-my-head calculation made when the reporter called me on<br />
the phone with no warning. Right ballpark, but not very accurate. Later I redid the calculation carefully.</blockquote><br />
<br />
Arnold's computations were similar to ours but he used a greater accuracy for the number of independent lotteries you have to buy to have a 50% chance of choosing the jackpot numbers at least once. His answer to this was 101,274,322. Using this, Arnold's estimate for the number of years, buying a ticket every minute, to have a 50% chance of winning a jackpot is193 years instead of our estimate of 192 years.<br />
<br />
Arnold said that he also estimated the expected value of a $1 ticket. To do this he needed an estimate for the number of tickets sold. He was told that a reasonable estimate was 106 million. In calculating the expected value of a $1 ticket he used the cash value of 164.4 million dollars instead of the annuity payout of 340 million dollars. He also took into account the possibility of having to share the jackpot. Doing this he got an expected value of exactly $1, just the price of the ticket. He commented that if he took into account the taxes the expected value would be more like 80 cents making even this lottery an unfavorable event.<br />
<br />
The news writers also gave a lot of coverage of Senator Gregg (Chairman of the Senate Budget Committee) winning $853,492 for getting the second highest prize: getting the 5 basic numbers correct but note the bonus number. Normally the prize for getting this is $200,000 cash but Gregg was the beneficiary of recent change in the powerball lottery. <br />
<br />
The powerball officials have found that increasing the size of the jackpot can increase the ticket sales because of the public's interest in large jackpots. They do this by increasing the number of possible basic numbers. When they started in 1992, to get the jackpot you had to get the 5 basic numbers chosen from 45 numbers and the 1 bonus number chosen from 45 number correct. Here are the changes so far<br />
<br />
<center><br />
1992 5 of 45 1 of 45<br><br />
1997 5 or 49 1 of 42<br><br />
2002 5 of 55 1 of 42<br><br />
2005 5 of 55 1 of 42<br><br />
</center><br />
<br />
While the lottery officials want to have higher jackpots, they also do not want too long a period between jackpots. Normally the increase in the size of the lottery, when no one wins the jackpot, is determined by the amount taken in in this unsuccessful drawing. This was recently changed so that, when a new record jackpot occurs and no-one wins it, at most 25 million dollars are added to the Jackot until someone wins the jackpot. The money save by this is added to the second prize.<br />
<br />
When the 340 million jackpot was won, 49 players had the five basic numbers correct but not the bonus numbers. For these winners the $200,000 prize had 653,492 added to their prize so they each won $853,492. If they chosen the Powerball play option for an extra $1 their $200,000 would have been multiplied by 2,3,4, or 5 with equal probabilities. Thus if Gregg had chosen the Powerball play option, and been lucky, he would have won 1,653,492 dollars that he could add to his 15 or so million dollars he has in stocks. <br />
<br />
===DISCUSSION===<br />
<br />
(1) Do you think it is fair to advertise the lottery prize as 340 million when the cash prize is only 164.4 million?<br />
<br />
(2) What is the probability of winning the second prize?<br />
<br />
(3) Assuming that the estimate 106 million for the number of tickets sold find the expected number of second prize winners.<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Mammograms Validated as Key in Cancer Fight==<br />
<br />
The ''New York Times'' [http://www.nytimes.com/2005/10/27/health/27breast.html reported] on October 27, 2005 on a new National Cancer Institute study that attributed a significant decrease in the death rate from breast cancer to mammogram screening tests. The study, published in the New England Journal of Medicine, found that from 28% to 65% of the sharp 24% decrease in breast cancer death rates from 1990 to 2000 was due to screening; the remainder was attributed to new drugs used to treat the disease.<br />
<br />
Prior to this study, the value of mammogram screening had been disputed, for several reasons. In the general population, the test results in a large proportion number of false positives, about 90%. Thus, many women who are cancer-free are subjected to unnecessary procedures. Also, approximately 30% of cancers that are detected and treated would not have progressed significantly. Unfortunately, it isn't possible to distinguish between these so-called ''indolent'' cancers and those that become life-threatening, so it is routine practice to treat them all.<br />
<br />
The new study suggests that the benefits of routine mammography are more certain than earlier believed, according to Don Berry, Chairman of the biostatistics department of M. D. Anderson Cancer Center, in Houston, Texas, and the lead author of the paper. He said that the new study for the first time properly separates the effects of therapy and screening. Nonetheless, he cautioned that mammography does pose risks, and recommended that women be counselled before screening.<br />
<br />
Contributed by Bill Jefferys<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div></div>Nano12https://www.causeweb.org/wiki/chance/index.php?title=Chance_News_7&diff=1558Chance News 72005-11-05T09:34:58Z<p>Nano12: /* Slices of risk and the <em>broken heart</em> concept */</p>
<hr />
<div>Sept 26 2005 to Oct 15 2005<br />
==Quotation==<br />
<blockquote><br />
While writing my book [Stochastic Processes] I had an argument with Feller [Introuction to Probability Theory and its Applications]. He asserted that everyone said "random variable" and I asserted that everyone said "chance variable." We obviously had to use the same name in our books, so we decided the issue by a stochastic procedure. That is, we tossed for it and he won. </blockquote><br />
<br />
<p align = right> Joe Doob<br><br />
[http://www.dartmouth.edu/~chance/Doob/conversation.html Statistical Science]<br><br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Forsooth==<br />
<br />
Peter Winkler suggested our first forsooth.<br />
<br />
<blockquote>Texas beats Ohio State in their opening game <br />
of the season (Saturday Sept 10 2002). The sportscasters (legendary Brent Musburger on play-by-play or Gary Danielson on analysis) observed that of the 14 teams who have <br />
previously played in the championship game (at the end of each season) 5 <br />
have suffered an earlier defeat. "Thus," they conclude, "Ohio State can <br />
still make it to the championship game, but their chances are now less <br />
than 50%."</blockquote><br />
<br />
===Discussion===<br />
<br />
What is wrong with this?<br />
----<br />
Here are forsooths from the September 2005 issues of RSS NEWS<br />
<br />
<blockquote>'Big ticket quiz' at the start of Wimbledon:<br><br><br />
Q. How many punnets (a small light basket or other container for fruit or vegetables) of strawberries are eaten each day during the Wimbledon tournament?<br><br />
Is it (a) over 8,000, (b) over 9,000 or (c) over 10,000?</blockquote><br />
<br />
<div align="right">BBC radio 5<br><br />
20 June 2005</div><br />
<br />
<blockquote>Waiting time for foot surgery down by 500%</blockquote><br />
<br />
<div align="right">Evening News (Edinburgh)<br><br />
5 July 2005</div><br />
<br />
The next two forsooths are from the October RSS news.<br />
<br />
<blockquote>In 1996-8 when the number attending university was static, the participation of women was also static, but male participation fell.</blockquote><br />
<br />
<div align="right">The Times Higher<br><br />
21 January 2005</div><br />
<br />
<blockquote>[On the subject of congestion on the London Underground..] 'Last year 976 million of us used the tube...'</blockquote><br />
<br />
<div align="right">BBC London News<br><br />
19 May 2005</div><br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Fortune's Formula==<br />
<br />
''Fortune's Formula: Wanna Bet?''<br><br />
''New York Times Book Section'', September 25, 2005<br><br />
David Pogue<br />
<br />
This must be the kind of review that every Science writer dreams of. Pogue ends his review with:<br />
<br />
<blockquote> ''Fortune's Formula'' may be the world's first history book, gambling primer, mathematics text, economics manual, personal finance guide and joke book in a single volume. Poundstone comes across like the best college professor you ever had, someone who can turn almost any technical topic into an entertaining and zesty lecture. But every now and then, you can't help wishing there were some teaching assistants on hand to help.</blockquote><br />
<br />
The author William Poundstone is a science writer who has written a number of very successful science books. His book, ''Prisoner's dilemma: John von Neumann, game theory and the puzzle of the bomb'', was written in the style of this book. Indeed Helen Joyce, in her review of this book in Plus Magazine writes:<br />
<br />
<blockquote>This book is a curious mixture of biography, history and mathematics, all neatly packaged into an entertaining and enlightening read. </blockquote><br />
<br />
Poundstone describes himself as a visual artist who does books as a "day job.". You can learn about his art work [http://www.uiowa.edu/~iareview/tirweb/feature/poundstone/interview2.htm here].<br />
<br />
''Fortune's Formula'' is primarily the story of Edward Thorp, Claude Shannon, and John Kelly and their attempt to use mathematics to make money gambling in casinos and on the stock market. None of these did their graduate work in mathematics. Thorp and Kelly got their Phd's in physics and Shannon in Genetics. <br />
<br />
In the spring of 1955, while a graduate student at UCLA, Thorp joined a discussion on the possiblity of making money from roulette. Thorp suggested that they could taking advantage of the fact that bets are still accepted for a few second after the croupier releases the ball, and in these seconds, he could estimate what part of the wheel the ball would stop. <br />
<br />
Thorp did not pursue this and in 1959 became an instructor in mathematics at M.I.T. Here he became interested in blackjack and developed his famous card counting method for wining at blackjack. He decided to publish his method in the most prestigious journal he could find and settled on ''Proceedings of the National Academy of Sciences''. For this he needed to have a member of the Academy submit his paper. The only member in the math department was Shannon so he had to persuade him of the importance of his paper. Shannon not only agreed but in the process became fascinated by Thorp's idea for beating roulette. He agreed to help Thorp carry this out. They built a roulette machine in Shannon's basement. It worked fine there in trial runs but not so well in the casino so they did not pursue this method of getting rich. <br />
<br />
Of course Thorp is best known for showing that blackjack is a favorable game and giving a method to exploit this fact. Shannon is best known for his work in information theory. Kelly is known his method for gambling in a favorable game. This plays a central role in Poundstone's book and is probably why Pogue felt that it would help if he had a teaching assistant. Poundstone tries to explain Kelly's work in many different ways but what he really needed to understand it is an example but this required too many formulas for a popular book. So we shall include an example from Chance News 7.09. <br />
<br />
Writing for Motley Fool, 3 April 1997 Mark Brady complained about the inumeracy of the general public and gave a number of examples including this one:<br />
<br />
<blockquote> Fear of uncertainty and innumeracy are synergistic. Most people cannot do the odds. What is a better deal over a year? A 100% safe return with 5 percent interest or a 90 percent safe return with a 20 percent return. For the first deal, your return will be 5% percent. For the second, your return will be 8%. Say you invest $1000 10 times. Your interest for the 9 successful deals will be 9000 x 0.2 or 1800. Subtract the 1000 you lost on the 10th deal and you get a $800 return on your original $10,000 for 8 percent.</blockquote><br />
<br />
Peter Doyle suggested that a better investment strategy in this case is:<br />
<br />
Faced with a 100 percent-safe investment returning 5 percent and a 90 percent-safe investment returning 20%, you should invest 20% of your funds in the risky investment and 80% in the safe investment. This gives you an effective return of roughly 5.31962607969968292 percent. <br />
<br />
Peter is using a money management system due to J. L. Kelly (1956: "A new interpretation of information rate," ''Bell System Technical Journal'', '''35'''). Kelly was interested in finding a rational way to invest your money faced with one or more investment schemes, each of which has a positive expected gain. He did not think it reasonable to try simply to maximize your expected return. If you did this in the Motley Fools example as suggested by Mark Brady, you would choose the risky investment and might well lose all your money the first year. We will illustrate what Kelly did propose in terms of Motley Fools example. <br />
<br />
We start with an initial capital, which we choose for convenience to be $1, and invest a fraction r of this money in the gamble and a fraction 1-r in the sure-thing. Then for the next year we use the same fractions to invest the money that resulted from the first year's investments and continue, using the same r each year. Assume, for example, that in the first and third years we win the gamble and in the second year we lose it. Then after 3 years our investment returns an amount f(r) where: <br />
<br />
<math><br />
f(r) = (1.2r + 1.05(1-r))(1.05(1-r))(1.2r + 1.05(1-r)). <br />
</math><br />
<br />
After n years, we would have n such factors, each corresponding to a win or a loss of our risky investment. Since the order of the terms does not matter our capital will be: <br />
<br />
<math><br />
f(r,n) = (1.2r + 1.05(1-r))^W(1.05(1-r))^L<br />
</math><br />
<br />
where W is the number of times we won the risky investment and L the number of times we lost it. Now Kelly calls the quantity:<br />
<br />
<math><br />
G(r) =\lim_{n \to \infty }\frac{\log(f( r,n)} {n}<br />
</math> <br />
<br />
the exponential rate of growth of our capital. In terms of G(r) our capital should grow like <math> e^{G(r)} </math>. In our example: <br />
<br />
<math><br />
\log(\frac{f(r,n)}{n}) = \frac{W}{n}\log(1.2r + 1.05(1-r)) + \frac{L}{n}\log(1.05(1-r))<br />
</math> <br />
<br />
Since we have a 90% chance of winning our gamble, the [http://en.wikipedia.org/wiki/Strong_law_of_large_numbers#The_strong_law strong law of large numbers] tells us that as n tends to infinity this will converge to <br />
<br />
<math><br />
G(r) = 0.9\log(1.2r + 1.05(1-r))+0.1\log(1.05(1-r))<br />
</math><br />
<br />
It is a simple calculus problem to show that G(r) is maximized by r = 0.2 with: <br />
G(0.2) = 0.05183. Then e^{0.05183} = 1.0532, showing that our maximum rate of growth is 5.32% as claimed by Peter. <br />
<br />
The attractiveness of the Kelly investment scheme is that, in the long run, any other investment strategy (including those where you are allowed to change your investment proportions at different times) will do less well. "In the long run and less well" means more precisely that the ratio of your return under the Kelly scheme and your return under any other strategy will tend to infinity.<br />
<br />
Thorp had a very good experience in the stock market, which is described very well by Gaeton Lion in his excellent [http://www.amazon.com/gp/product/customer-reviews/0809046377/ref=cm_cr_dp_pt/103-8647004-5865443?%5Fencoding=UTF8&n=283155&s=books review] of ''Fortune's Formula''. He writes:<br />
<br />
<blockquote> Ed Thorp succeeded in deriving superior returns in both gambling and investing. But, it was not so much because of Kelly's formula. He developed other tools to achieve superior returns. In gambling, Ed Thorp succeeded at Black Jack by developing the card counting method. He just used intuitively Kelly's formula to increase his bets whenever the odds were in his favor. Later, he ran a hedge fund for 20 years until the late 80s and earned a rate of return of 14% handily beating the market's 8% during the period. <br><br><br />
<br />
Also, his hedge fund hardly lost any value on black Monday in October 1987, when the market crashed by 22%. The volatility of his returns was far lower than the market. He did this by exploiting market inefficiencies using warrants, options, and convertible bonds. The Kelly formula was for him a risk management discipline and not a direct source of excess return. </blockquote><br />
<br />
Shannon also made a lot of money on the stock market, but did not use Kelly's formula. In his [http://www.amazon.com/gp/product/customer-reviews/0809046377/ref=cm_cr_dp_pt/103-8647004-5865443?%5Fencoding=UTF8&n=283155&s=books review] Gaeton Lion writes<br />
<br />
<blockquote>Claude Shannon amassed large wealth by recording one of the best investment records. His performance had little to do with Kelly's formula. Between 1966 and 1986, his record beat even Warren Buffet (28% to 27% respectively). Shannon strategy was similar to Buffet. Both their stock portfolios were concentrated, and held for the long term. Shannon achieved his record by holding mainly three stocks (Teledyne, Motorola, and HP). The difference between the two was that Shannon invested in technology because he understood it well, while Buffet did not. </blockquote><br />
<br />
Finally, Thorp provided the following comments for the book cover:<br />
<br />
<blockquote>From bookies to billionaires, you'll meet a motley cast of characters in this highly original, 'outside the box' look at gambling and investing. Read it for the stories alone, and you'll be surprised at how much else you can learn without even trying. --Edward O. Thorp, author of ''Beat the Dealer'' and ''Beat the Market''.</blockquote><br />
<br />
Submitted by Laurie Snell.<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Which foods prevent cancer?==<br />
<br />
Which of these foods will stop cancer? (Not so fast)<br><br />
New York Times, 27 September 2005, Sect. F, p. 1<Br><br />
Gina Kolata<br />
<br />
Among other examples, the article includes a [http://www.nytimes.com/imagepages/2005/09/26/science/20050927_CANCER_GRAPHIC.html data graphic] on purported benefits of dietary fiber in preventing colorectal cancer. Early observational studies indicated an association, but subsequent randomized experiments found no effect. <br />
<br />
More to follow.<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Slices of risk and the <em>broken heart</em> concept==<br />
[http://www.gloriamundi.org/picsresources/news20050912.pdf How a Formula Ignited Market That Burned Some Big Investors],<br />
Mark Whitehouse, The Wall Street Journal, September 12, 2005.<br><br />
<br />
This on-line article relates how a statistician, David Li,<br />
unknown outside a small coterie of finance theorists, helped change the world of investing. <br />
<br />
The article focuses on a event last May when General Motors Corp's debt<br />
was downgraded to junk status, causing turmoil in some financial markets.<br />
The article gives a nice summary of the underlying financial instruments known<br />
as credit derivatives -<br />
investment contracts structured so their value depends on the behavior of some other thing or event -<br />
with exotic names like <br />
[http://en.wikipedia.org/wiki/Collateralized_debt_obligations collateralized debt obligations] and [http://en.wikipedia.org/wiki/Credit_default_swap credit-default swaps].<br />
<br />
The critical step is to estimate the likelihood that many of the companies <br />
in a pool of companies would go bust at once. <br />
For instance, if the companies were all in closely related industries,<br />
such as auto-parts suppliers, they might fall like dominoes after a catastrophic event.<br />
Such a pool would have a 'high default correlation'.<br />
<br />
In 1997, nobody knew how to calculate default correlations with any precision. <br />
Mr. Li's solution drew inspiration from a concept in actuarial science known as the <br />
<em>broken heart</em> syndrome - people tend to die faster after the death of a beloved spouse. <br />
Some of his colleagues from academia were working on a way to predict this<br />
death correlation, something quite useful to companies that sell life insurance and joint annuities.<br />
He says:<br />
<blockquote><br />
Suddenly I thought that the problem I was trying to solve was exactly like the problem these<br />
guys were trying to solve,.<br />
Default is like the death of a company, so we should<br />
model this the same way we model human life."<br />
</blockquote><br />
<br />
This gave him the idea of using [http://en.wikipedia.org/wiki/Copula_%28statistics%29 copulas], <br />
mathematical functions the colleagues had begun applying to actuarial science. <br />
Copulas help predict the likelihood of various events<br />
occurring when those events depend to some extent on one another. <br />
Until the events last May of this year, one of the most popular copulas for bond pools <br />
was the Gaussian copula, named after <br />
[http://en.wikipedia.org/wiki/Carl_Friedrich_Gauss Carl Friedrich Gauss], a 19th-century German statistician. <br />
<br />
===Further reading===<br />
* The [http://www.gloriamundi.org/picsresources/news20050912.pdf on-line article] gives more details about what went wrong in the financial markets in May and the search for a more appropriate copula to capture better the <em>broken heart</em> syndrome between companies.<br />
* [http://en.wikipedia.org/wiki/Wikipedia Wikipedia] is a very worthwhile on-line resource for definitions of technical words, such as [http://en.wikipedia.org/wiki/Copula_%28statistics%29 copula].<br />
<br />
Submitted by John Gavin.<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Learning to speak via statistics and graph theory==<br />
<br />
[http://education.guardian.co.uk/tefl/teaching/story/0,15085,1576100,00.html Computer learns grammar by crunching sentences], Max de Lotbinière September 23, 2005, [http://www.guardianweekly.co.uk/ Guardian Weekly].<br><br />
[http://www.cornellsun.com/vnews/display.v/ART/2005/09/09/432118a84f6af Profs’ New Software ‘Learns’ Languages], Ben Birnbaum, 9 Sep 2005, Cornell Daily Sun.<br />
<br />
A language-learning robot may sound like science fiction but new software, developed by Cornell University psychology professor Shimon Edelman, with colleagues Zach Solan, David Horn and Eytan Ruppin from Tel Aviv University in Israel, is well on the way to constructing a computer program that can teach itself languages and make up its own sentences, the developers' claim.<br />
<br />
Unlike previous attempts at developing computer algorithms for language learning - "Automatic Distillation of Structure," or "ADIOS" for short - discovers complex patterns in raw text by repeatedly aligning sentences and looking for overlapping parts.<br />
Once it has derived a language's rules of grammar,<br />
it can then produce sentences of its own, simply from blocks of text in that language.<br />
<br />
It has been evaluated on artificial context-free grammars with thousands of rules, <br />
on natural languages as diverse as English and Chinese, <br />
on coding regions in DNA sequences and on protein data correlating sequence with function. <br />
<br />
Edelman comments:<br />
<blockquote><br />
Adios relies on a statistical method for pattern extraction and on structured generalisations <br />
- the two processes that have been implicated in language acquisition.<br />
Our experiments show that Adios can acquire intricate structures <br />
from raw data including transcripts of parents' speech directed at two- or three-year-olds.<br />
This may eventually help researchers understand how children, <br />
who learn language in a similar item-by-item fashion, and with little supervision, <br />
eventually master the full complexity of their native tongue.<br />
</blockquote><br />
<br />
[http://plus.maths.org/latestnews/may-aug05/adios/ Plus Magazine's website]<br />
offers a more logical explanation:<br />
<blockquote><br />
The ADIOS algorithm is based on statistical and algebraic methods performed on one of the most basic and versatile objects of mathematics - the graph.<br />
Given a text, the program loads it as a graph by representing each word by a node, or vertex, and each sentence by a sequence of nodes connected by lines. A string of words in the text is now represented by a path in the graph. <br><br />
<br />
Next it performs a statistical analysis to see which paths, or strings of words, occur unusually often. <br />
It then decides that those that appear most frequently - called "significant patterns" - <br />
can safely be regarded as a single unit<br />
and replaces the set of vertices in each of these patterns by a single vertex, <br />
thus creating a new, generalised, graph.<br><br />
<br />
Finally, the program looks for paths in the graph which just differ by one vertex. <br />
These stand for parts of sentences that just differ by one word (or compound of words) like "the cat is hungry" and "the dog is hungry". <br />
Performing another statistical test on the frequency of these paths, the program identifies classes of vertices, or words, that can be regarded as interchangeable, or equivalent. <br />
The sentence involved is legitimate no matter which of the words in the class - in our example "cat" or "dog" - you put in.<br><br />
<br />
This last step is then repeated recursively.<br><br />
</blockquote><br />
<br />
[http://plus.maths.org/latestnews/may-aug05/adios/ The website] uses graphs to illustrate some examples and it finishes with some reassuring words:<br />
<blockquote><br />
All this doesn't mean, of course, that the program actually "understands" what it's saying. It simply knows how to have a good go at piecing together fragments of sentences it has identified, in the hope that they are grammatically correct. So if, like me, you're prone to swearing at your computer, you can safely continue to do so: it won't answer back for a long while yet.<br />
</blockquote><br />
<br />
===Further reading===<br />
The [http://adios.tau.ac.il/ ADIOS homepage] offers an overview and more detailed description of the program.<br />
<br />
Submitted by John Gavin.<br />
<br />
==Understanding probability==<br />
<br />
Understanding Probability:Chance rules in everyday life<br><br />
Cambridge University Press 2004<br><br />
Henk Tijms<br />
<br />
Hank Tijms is Professor in Operation Research at the Vrije University in Amsterdam. This book is based on his earlier Dutch book “Spelen met Kansen.” <br />
<br />
The aim of this book is to show how probability applies to our everyday life in a way that your Uncle George could understand even if he has forgotten much of his high school math. Tijms does not try to avoid mathematics but only to postpone the formal math until the reader has seen the many applications of probability in the real world, how much fun it is, and learned to work problems and when he can’t work one how to get the answer by simulation. He learns all this in part I of the book and then he learns the more formal math in Part II.<br />
<br />
In Chapter 1 Tijms asks the reader to think about problems with surprising answers in the spirit of Susan Holmes “[http://www-stat.stanford.edu/~susan/surprise/ Probability by Surprise]” including the birthday problem and the Monty Hall problem. Readers are on their own to try to solve one or more of the problems but promised that they will see the solutions later in the book. <br />
<br />
Chapter 2 deals with the law of large numbers and introduces the concept of simulation. This theorem is explained and illustrated by problems related, for example, to coin tossing, random walks and casino games. Expected value is introduced in an informal way to be defined more carefully later in the book. For the reader who is not frightened by mathematical formulas, Tijms includes a discussion of the Kelly betting system with a footnote saying that this paragraph can be skipped at first reading. This is a fascinating topic that is widely applied in gambling and stock investment but rarely appears in a probability book.<br />
<br />
In Chapter 3 the author returns to previous problems such as the birthday problem and gambling systems and solves them first by simulation and then by mathematics. <br />
<br />
In this chapter Tijms describes Efron’s bootstrap method and uses it to solve a number of problems including a hypothetical clinical trial and to test if the famous 1970 draft lottery during the Vietnam War was fair. Again the bootstrap method has wide application but rarely occurs in an elementary probability or statistics book.<br />
<br />
Chapter 4 describes the binomial, Poisson, and hypergeomtric distributions and how to use them in solving problems such as the famous hat check problem, and a variety of interesting lottery questions. The Poisson process is discussed but again with the footnote that novice readers might want to read this at a later time.<br />
<br />
Chapter 5 is mainly about Center Limit Theorem and its many applications especially to statistics. <br />
<br />
Chapter 6 introduces Chance trees and Bayes’s rule. The tree method is used to explain a variety of problems including the Monty Hall Problem and the false-positive paradox. <br />
<br />
This is a brief description of the first six chapters which constitute Part I of the book. Now the fun is over. Part 2 called “Essentials of probability” looks like the traditional first chapters in a standard probability book. But the reader has already found how exciting probability is, has a good intuitive idea of the basic concepts and has worked many of the interesting problems at the end of each chapter either using math or simulation. For some students this might allow them to actually enjoy Part 2. But your Uncle George may want to quit while they are ahead. <br />
<br />
Tijms writes with great clarity and his enthusiasm for probability in the real world is contagious. We were delighted to see, as acknowledged in the preface, that Tijms included several of the more interesting problems discussed in Chance News, often going well beyond what we had said in our discussion of the problem. <br />
<br />
This book presents a completely new way to go about teaching a first course in probability and we think those who teach such a course should consider trying it out.<br />
<br />
===Discussion===<br />
<br />
(1) In the days of Basic we required all students to learn Basic in their first math course so we could assume that students could write programs to simulate probability problems and so me made heavy use of simulation as suggested in this book. The author uses Pascal in his book. What present language do you think is easiest for a student with no computing experience to learn?<br />
<br />
We asked Professor Tijms what the situation was in math departments in Europe and he replied:<br />
<br />
<blockquote>In math departments of universities and polytechnic schools in Europe students learn to write computer programs. In my university they still learn to program in Java and C++ ( in previous days Pascal), but I see in the Netherlands the trend that the instructors think it is sufficient if the students are able to program in Matlab. <br><br><br />
<br />
In ny book I have chosen to formulate the simulation programs in Pascal because of the clarity and the simplicity of the language, though this language is hardly used anymore. The introductory probability course at my university is given before they have learned to program, but this does not prevent them of simulating probability problems by using Excel. In the simulation of many elementary probability problems a random-number generator alone suffices to simulate those problems and so Excel can be used. In the second year they have mastered Matlab, a perfect tool with its excellent graphics to simulate many challenging probability problems ( they really like it, in particular when it concerns problems such as the problems 2.24-2.45 in chapter 2 and the problems 5.11-5.13 in chapter 5). <br />
</blockquote><br />
<br />
<br />
(2) Do you think that probability books should include data to test probability models that are said to describe real world problems? If so name some models that you think would pass such a test and some that you think might not.<br />
<br />
Submitted by Laurie Snell<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Societies worse off when they have God on their side==<br />
<br />
[http://www.timesonline.co.uk/article/0,,2-1798944,00.html Societies worse off when they have God on their side]<br><br />
Timesonline, September 27, 2005<br><br />
Ruth Gledhill<br />
<br />
[http://moses.creighton.edu/JRS/2005/2005-11.html Cross-national correlations of quantifiable societal health with popular religiosity and secularism in the prosperous democracies]<br><br />
Journal of Religion & Society, Vol.7(2005)<br><br />
Gregory S. Paul<br />
<br />
In the Times article we read:<br />
<br />
<blockquote>According to the study, belief in and worship of God are not only unnecessary for a healthy society but may actually contribute to social problems.<br><br><br />
Many liberal Christians and believers of other faiths hold that religious belief is socially beneficial, believing that it helps to lower rates of violent crime, murder, suicide, sexual promiscuity and abortion. The benefits of religious belief to a society have been described as its “spiritual capital”. But the study claims that the devotion of many in the US may actually contribute to its ills. <br />
</blockquote><br />
<br />
Gregory Paul is a dinosaur paleontologist and on an [http://www.abc.net.au/worldtoday/indexes/2005/twt_20050928.htm interview] on Australian ABC radio Paul said that, being a paleontologist, for many years he had to deal with the issue of creationism versus evolutionary science in the U.S and his interest in evolutionary science prompted him to look at whether there was any link between the religiosity of a society and how well that society functions. <br />
<br />
If you look at Paul's article you will find very little technical statistical analysis, for example, he did not carry out a regression analysis. Rather he rests his case on the series of scatterplots.<br />
<br />
Paul describes his data sources as:<br />
<br />
<blockquote>Data sources for rates of religious belief and practice as well as acceptance of evolution are the 1993 Environment I (Bishop) and 1998 Religion II polls conducted by the International Social Survey Program (ISSP), a cross-national collaboration on social science surveys using standard methodologies that currently involves 38 nations. The last survey interviewed approximately 23,000 people in almost all (17) of the developed democracies; Portugal is also plotted as an example of a second world European democracy. Results for western and eastern Germany are combined following the regions' populations. England is generally Great Britain excluding Northern Ireland; Holland is all of the Netherlands. The results largely agree with national surveys on the same subjects; for example, both ISSP and Gallup indicate that absolute plus less certain believers in a higher power are about 90% of the U.S. population. The plots include Bible literalism and frequency of prayer and service attendance, as well as absolute belief in a creator, in order to examine religiosity in terms of ardency, conservatism, and activities. </blockquote><br />
<br />
Here are the countries Paul considered with the abbreviations used on the graphics. <br />
<br />
A = Australia, C = Canada, D = Denmark, E = Great Britain, F = France, G = Germany,<br />
H = Holland, I = Ireland, J = Japan, L = Switzerland, N = Norway, P = Portugal, R = Austria,<br />
S = Spain, T = Italy, U = United States, W = Sweden, Z = New Zealand.<br />
<br />
There seems to be no agreement as to which countries are developed democracies. For example Paul might have included Greece and Belgium, Finland, and others but the data may have determined his choice. Paul comments that he added Portugal as an example of a second world democracy. <br />
<br />
Paul's anaysis of the data includes a series of 9 Figures which are available at the end of the article and are the most interesting part of the study. If you try printing Paul's article you will only get the first of his 9 Figures. When you look at the [http://moses.creighton.edu/JRS/2005/2005-11.html web version] you will still see only Figure 1 but the others can be viewed by selecting the numbers from 2 to 9 on the left side of Figure 1.<br />
<br />
Figure 1 deals with the proportion of people who accept human evolution which is interesting but not as relevant to the welfare of the people as others so we will look at Figure 2.<br />
<br />
[[Image:religion2.png|500px|center|Source:Gregory Paul]]<br />
<br />
Each Figure iprovides 5 separate scatterplots. Ïn Figure 2 we see that the U.S. has largest number--between 6 and 7-- of homicides per 100,000 and Spain has the lowest number with less than 1 homicide per 100,000. We also see that the U.S. has the highest proportion of people, about 25%, who take the bible literally while several countries have less than 10% such people.<br />
<br />
What we cannot do is compare the number of homicides per thousand between those who take the bible literally and those who are agnostics or atheists which is what we would really want to know. Presumably the data did not permit this comparison. <br />
<br />
[[Image:religion3.png|500px|center|Source:Gregory Paul]]<br />
<br />
Figure 3 deals with "14-24 year old suicides per 100,000". Here the U.S. is in about the middle.<br />
<br />
Figure 4 deals with the "under-five mortalities per 1000 births".<br />
<br />
[[Image:religion4.png|500px|center|Source:Gregory Paul]]<br />
<br />
Ignoring Portugal, the U.S. has the highest number of under-five mortalities per 1000 births-- between 7 and--8 while several countries have only 4.<br />
<br />
The other figures can be seen at end of Paul's article. They deal with life expectancy, sexually transmitted diseases, abortion and 15-16 year old pregnancies. Life expectancy is the smallest in the U.S. and for sexually transmitted diseases, abortion and 15-17 year old prenacies the U.S. is at the top of the graphs and in fact these look like outliers.<br />
<br />
Well, this study does not by itself justify the Times hedline: "Societies worse off when they have God on their side." Paul himself would not claim this. He writes:<br />
<br />
<blockquote> This study is a first, brief look at an important subject that has been almost entirely neglected by social scientists. The primary intent is to present basic correlations of the elemental data. Some conclusions that can be gleaned from the plots are outlined. This is not an attempt to present a definitive study that establishes cause versus effect between religiosity, secularism and societal health. It is hoped that these original correlations and results will spark future research and debate on the issue.</block<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div></div>Nano12https://www.causeweb.org/wiki/chance/index.php?title=Chance_News_9&diff=1557Chance News 92005-11-05T09:34:55Z<p>Nano12: /* Questions */</p>
<hr />
<div>==Quotation==<br />
Å quotation will be added here.<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Forsooth==<br />
Forsooth items should be added here.<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Supreme Court Nominee Alito: Statistics Misleading?==<br />
An [http://www.salon.com/politics/war_room/2005/10/31/jury/index.html article] in Salon.com for October 31 discusses the first-degree murder trial, Riley v. Taylor. The defendant Riley was African-American; at the trial, the prosecution used its peremptory challenges to eliminate all three of the African-Americans on the jury panel. In the same county that year, there were three other first-degree murder trials, and in every one of those cases all of the African-American jurors were struck.<br />
<br />
A majority of the judges on the appeals court thought that there was evidence that jurors were struck for racial reasons. According to them, a simple calculation indicates that there should have been five African-American jurors amongst the forty-eight that were empanelled. However, there were none. To these judges, this was clear evidence of racial motivaion in the striking of such jurors.<br />
<br />
Judge Alito dissented. He called the majority's analysis simplistic, and stated that although only 10% of the U.S. population is left-handed, five of the last six people elected president of the United States were left-handed. He asked rhetorically whether this indicated bias against right-handers amongst the U.S. electorate.<br />
<br />
The majority responded that there is no provision in the Constitution that protects persons from discrimination based on whether they are right-handed or left-handed, and that to compare these cases with the handedness of presidents ignores the history of racial discrimination in the United States.<br />
<br />
===Questions===<br />
<br />
1) Assuming that Judge Alito is correct about the proportion of left-handers in the U.S. population, what is the probability that five of the last six presidents elected would be left-handed?<br />
<br />
2) Is Judge Alito's comparison biased by the fact that he chose just the last six presidents? Presumably he believed that the president just before this group was right-handed, otherwise he would have included him in the sample and said "six of the last seven presidents." What is the relevant statistic?<br />
<br />
3) When the decision came down in 2001, the last six people elected president were George W. Bush, Clinton, George H. W. Bush, Reagan, Carter and Nixon. Of these, Clinton and George H. W. Bush were left-handed. Ford, who was left-handed, was not elected president (or even vice-president); he became president upon the resignation of Richard Nixon. Reagan may have been left-handed as a child, but he wrote right-handed so his case isn't clear; the Reagan Presidential Library [http://www.reagan.utexas.edu/archives/reference/facts.html says] that he was "generally right-handed." Judge Alito may have been confused, including on his list Ford (who was not elected) and George W. Bush (who is not left-handed, although his father is), as well as Reagan. The other left-handed presidents were Truman and Garfield. Hoover is found on some lists of left-handed presidents, but according to the Hoover Institution, he was not left-handed. How does this information affect Alito's argument?<br />
<br />
4) Suppose that 5/48 of the jury pool were African-American. What is the probability that no juror amongst the 48 selected would have been African-American? How does this compare with the actual statistics of left-handed presidents? Does the same objection apply to this case as might apply to Alito's example?<br />
<br />
5) What is your opinion? Is there clear statistical evidence of racial bias in the use of peremptory challenges in this county?<br />
<br />
6) What does it say about our judiciary that Judge Alito could get his facts as wrong as he did, and that none of the judges in the majority caught the errors?<br />
<br />
Contributed by Bill Jefferys<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==item2==<br />
Replace item2 by the name of your article.</div>Nano12https://www.causeweb.org/wiki/chance/index.php?title=Chance_News_8&diff=1556Chance News 82005-11-05T09:34:52Z<p>Nano12: /* Possible Cancer Cluster in Connecticut */</p>
<hr />
<div>Oct 15 to Oct 30<br />
<br />
==Quotation==<br />
<blockquote>One more fagot of these adamantine bandages, is, the new science of Statistics. It is a rule, that the most casual and extraordinary events -- if the basis of population is broad enough -- become matter of fixed calculation. It would not be safe to say when a captain like Bonaparte, a singer like Jenny Lind, or a navigator like Bowditch, would be born in Boston: but, on a population of twenty or two hundred millions, something like accuracy may be had. Ralph Waldo Emerson Fate</blockquote><br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Forsooth==<br />
Here's another Forsooth from the October issue of RSS News.<br />
<blockquote>Your'e more likely to die in a fire in Strathclyde than anywhere else in the country</blockquote><br />
<br />
<div align="right">BBC1 mews bullietin<br><br />
11 May 2005</div><br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==The Poisson distribution and the Supreme Court==<br />
The Poisson distribution and the Supreme Court<br><br />
''Journal of the American Statistical Association'' 31, no. 195 ,(1936), 376-80<br><br />
W. Allen Wallis<br />
<br />
Supreme Court Appointments as a Poisson distribution<br><br />
''American Journal of Political Science'', 26, No.1, February 1982<br><br />
S. Sidney Ulmer<br />
<br />
This is not current news, but since Supreme Court appointments are in the news we felt that these articles might make an interesting class discussion.<br />
<br />
In 1936 statistician Allen Wallis suggested that a Poisson distribution can approximate the number of U.S. Supreme Court appointments in a given year. In his Table 1 Wallis provided the number appointed in each year over the intervals with different numbers of Justices on the Supreme Court: 1790-1806 (6) 1807-1836 (7), and 1837-1932 (9). Actually there were 10 in the years 1963 to 1967 which Wallis called "negligible exceptions."<br />
<br />
[[Image:wallis1.png|500px|center]]<br />
<br />
Wallis then restricts himself to the years 1837-1932 and finds that a Poisson distribution with mean .5 can approximate the number of court appointments in a year. His results are shown in his Figure II:<br />
<br />
[[Image:wallis2.png|500px|center]]<br />
<br />
In his article, Sidney Ulmer updated the data to 1980 and also includes data from the early Supreme Courts with 6 and 7 members. Thus his data covers the years 1790--1980. His Table 1 compares the actual number of appointments in a year with the expected number of appointments assuming a Poisson distribution with mean 5.13.<br />
<br />
[[Image:ulmer1.png|500px|center]]<br />
<br />
In his Table II Ulmer limits the data to the 9 member Supreme Courts: 1837 to 1862 and 1869-1980).<br />
<br />
[[Image:ulmer2.png|500px|center]]<br />
<br />
Testing the goodness of fits, Ulmer argues that the fit with the varying size Supreme Courts is just as good as with fixed size Supreme Courts.<br />
<br />
===DISCUSSION===<br />
<br />
(1) What is the probability that a President will make 2 or more appointments to the Supreme Court during a 4-year term? What is the probability a President makes no appointments during a 4-year term? Has this ever happened?<br />
<br />
(2) Do you agree with Ulmer that there is no reason to limit the data to years with the Supreme Court is the same size?<br />
<br />
(3) Obtain the data needed to update Ulmer's results to today and provide Tables that correspond to Ulmer's Tables 1 and 2. Add your Tables to this Chance News and make your data available to make it easier to update this in future years.<br />
<br />
Contributed by Laurie Snell<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Possible Cancer Cluster in Connecticut==<br />
Pratt Agrees to Increase Funding for Brain Cancer Study <br><br />
''The Associated Press''<br><br />
October 11, 2005<br><br />
Stephen Singer<br><br />
<br />
<br />
In a case that seems eerily familiar to the leukemia cancer cluster made famous by the book and movie, ''A Civil Action'', researchers are trying to determine whether or not a cancer cluster exists among workers at Pratt & Whitney, a company that manufactures jet engines. Over one hundred former or current Pratt & Whitney employees have been identified as having a relatively rare type of fatal brain tumor known as glioblastoma multiforme, which strikes 3 people per 100,000 every year. Many of these workers have been exposed to metals and chemical substances, including TCE (trichloroethylene), which is an engine degreaser. TCE is the same carcinogenic chemical that was dumped in the 1960’s and 1970’s by the chemical company, WR Grace, in Woburn, MA, and that was found to have contaminated the drinking water in two of the town’s wells. <br><br />
<br />
<br />
Prior to the recent announcement that the funding is being increased from $6 million dollars to $12 million dollars, this medical study was already being described as the largest occupational health study ever conducted. It covers 250,000 people who worked at any of the seven Connecticut Pratt & Whitney plants from 1952 to 2001. So far, at least 125 cases of brain cancer have been documented, according to the lawyer who represents dozens of individuals and family members.<br><br />
<br />
<br />
The study falls under the auspices of the Connecticut Department of Public Health. However, due to the overwhelming cost and scope of the study, Pratt & Whitney is funding the project. Since Pratt is paying for the study, they chose the researchers, a team from the University of Pittsburgh. The project began three years ago, and the results are expected to be available between 2007 and 2009.<br><br />
<br />
<br />
In the meantime, this case faces many of the obstacles common in the quest to establish whether or not a cancer cluster exists, such as proving causation, the fact that it can take a long time (sometimes 5-40 years) after exposure for true problems to show up, and finding the people who were exposed & convincing them to participate in the study. Additionally, there are legal difficulties for the families involved, including Connecticut’s statute of limitations laws, the length of time it takes investigators to reach a conclusion, the cost of litigation, and the “deep pockets” of a company like Pratt & Whitney.<br><br />
<br />
<br />
This case study provides a current example of an ongoing investigation into a possible cancer cluster. Will it ultimately be found to be a coincidence cluster or proven to be a true cancer cluster? Does it make sense that the researchers are including in the study everyone who worked at Pratt over a fifty year period, even those who only worked there for a brief time period and those who were not directly exposed to toxic substances (i.e. office workers)? Could the researchers possibly have an unconscious bias in favor of the company that is funding their research? If the company doesn’t fund the research, then who should? Is there some other way to structure such investigations, so that the company involved pays for the study, but is not allowed to choose the researchers and directly fund them?<br><br />
<br />
<br />
'''Further Reading'''<br><br />
<br />
• “Rare Cancer Found in Workers”, ''The New York Times'', March 10, 2002, Jane Gordon<br><br />
• “Scientist: Pratt Commits to Cancer Study”, ''The Hartford Courant'', May 19, 2005<br><br />
• “Participation in Cancer Study at Pratt Lagging”, ''The Hartford Courant'', October 12, 2005, Paul Marks<br><br />
• ''The New Haven Advocate'' has had more than a dozen articles that explain the working conditions at Pratt & Whitney, and also chronicle the history & progression of this case. These articles have been investigated and written primarily by Carole Bass, Associate Editor. A few of the articles are listed below. <br> <br />
-“Worked to Death”, August 2, 2001, Carole Bass & Camille Jackson<br><br />
-“Talking Cure”, October 28, 2004, Dave Goldberg<br><br />
-“Time’s Not on Their Side”, January 20, 2005, Carole Bass<br><br />
-“The Brains Behind the Brain”, October 20, 2005, Carole Bass <br><br />
For the early New Haven Advocate articles (i.e., 2001-2002) on this subject, go to http://old.newhavenadvocate.com/workedtodeath/index.html<br> <br />
For the articles since 2002, go to <br><br />
http://www.newhavenadvocate.com and search for Pratt & Whitney.<br><br />
<br />
Submitted by Josephine Rodriguez.<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==A record powerball lottery jackpot==<br />
<br />
On Saturday Oct 22, 2005 the powerball lottery had a record powerball jackpot of 340 million dollars. <br />
<br />
When you buy a ticket for this lottery, you specify five distinct numbers from 1 to 55, which we call basic numbers and one number from 1 to 42 called the bonus number. To win the Jackpot your 5 basic numbers and your bonus number must agree with a random choice of 5 basic numbers and one bonus number chosen by the lottery officials. The number of possible tickets is:<br />
<br />
<center><math>{55 \choose 5} 42 = </math> 146,107,962</center><br />
<br />
Thus if you buy a single ticket, the probability of having a winning jackpot ticket is<br />
<br />
<center> <math>{1} \over {146107962}</math> = .000000006844...</center><br />
<br />
The powerball website and the media expresses this by saying that the odds that you have a winning jackpot ticket is 1 in 146,107,962. <br />
<br />
Whenever there is a record jackpot, the news writers look for suggestions for other rare events that might be more familiar to its readers. <br />
<br />
Our own favorite was suggested by Fred Hoppe: if you toss a coin 27 times your chance of getting 27 heads in a row is greater than your chance of having a winning jackpot ticket when you buy a single ticket. (<math> 2^{27} = 134217728</math> and so there are 134,217,728 possible sequences of heads and tails and only 1 has all heads.)<br />
<br />
In an article for the ''Omaha World-Herald'' Oct 18, 2005 , Robynn Tysver writes:<br />
<br />
<blockquote> You have a greater chance of getting killed by lightning than winning this week's 340 million Powerball jackpot. You also have a greater chance of drowning in a bathtub. The lifetime odds of getting killed by lightning are one in 56,439, and the lifetime odds of dying while in or falling into a bathtub are one in 10,582, according to the National Safety Council. <br />
</blockquote><br />
<br />
These are not even in the ballpark. The ''Minneapolis Star Tribune'' consulted mathematicians David Bressoud and Douglas Arnold who contributed the following:<br />
<br />
According to Arnold you have a seven times better chance of becoming a saint. And Bressoud notes that you're six times more likely to get elected president of the United States. But they also provide the following more interesting estimates:<br />
<br />
<blockquote>Bressoud: "If you buy 10 tickets a week, every week, it would take you 280,000 years before you could expect to win."<br><br><br />
<br />
Arnold: "If you were to select a group of Powerball numbers every minute for 138 years, you would have about a 50 percent chance of picking the winning Powerball ticket." <br><br><br />
<br />
It is not clear what Bressoud means by "expect to win". We can check this by a simple calculation (simple for Mathematica). Let q(n) be the probability that you if you buy n tickets you fail to get a winning jackpot ticket . Then:<br />
<br />
<center> <math> \left(\frac{146107961}{146107962}\right) ^n = q(n) </math></center><br />
<br />
The average number of weeks in a year is 52.177457 so If you buy 10 tickets a week, every week for 280,000 years you will buy about 146,097,000 tickets. Using this number for n in our formula we find that you have about a 37% chance of not getting a winning lottery ticket or a 63% chance of getting one. We would not "expect to win" with a 63% chance of winning but others may. Using our formula for q(n) we find that if we buy 10 tickets a week, every week for 830,000 years you will have about a 95% chance of getting at least one winning lottery ticket which seems to us more appropriate for expecting to win. <br />
<br />
Consider now Arnold's example. Our colleague Dana Williams found that you need to buy a ticket for about 101 million lottery offerings to have about a 50% chance of getting at least one winning lottery ticket. There are an average of 525,946.766 minutes in a year. Dividing 101 million by this number gives 192.035. Thus Arnold's 138 years should be 192 years.<br />
<br />
We asked Professor Arnold about this and he replied:<br />
<br />
<blockquote> That number, which was quoted in the ''Star Tribune'' was an off-the-top-of-my-head calculation made when the reporter called me on<br />
the phone with no warning. Right ballpark, but not very accurate. Later I redid the calculation carefully.</blockquote><br />
<br />
Arnold's computations were similar to ours but he used a greater accuracy for the number of independent lotteries you have to buy to have a 50% chance of choosing the jackpot numbers at least once. His answer to this was 101,274,322. Using this, Arnold's estimate for the number of years, buying a ticket every minute, to have a 50% chance of winning a jackpot is193 years instead of our estimate of 192 years.<br />
<br />
Arnold said that he also estimated the expected value of a $1 ticket. To do this he needed an estimate for the number of tickets sold. He was told that a reasonable estimate was 106 million. In calculating the expected value of a $1 ticket he used the cash value of 164.4 million dollars instead of the annuity payout of 340 million dollars. He also took into account the possibility of having to share the jackpot. Doing this he got an expected value of exactly $1, just the price of the ticket. He commented that if he took into account the taxes the expected value would be more like 80 cents making even this lottery an unfavorable event.<br />
<br />
The news writers also gave a lot of coverage of Senator Gregg (Chairman of the Senate Budget Committee) winning $853,492 for getting the second highest prize: getting the 5 basic numbers correct but note the bonus number. Normally the prize for getting this is $200,000 cash but Gregg was the beneficiary of recent change in the powerball lottery. <br />
<br />
The powerball officials have found that increasing the size of the jackpot can increase the ticket sales because of the public's interest in large jackpots. They do this by increasing the number of possible basic numbers. When they started in 1992, to get the jackpot you had to get the 5 basic numbers chosen from 45 numbers and the 1 bonus number chosen from 45 number correct. Here are the changes so far<br />
<br />
<center><br />
1992 5 of 45 1 of 45<br><br />
1997 5 or 49 1 of 42<br><br />
2002 5 of 55 1 of 42<br><br />
2005 5 of 55 1 of 42<br><br />
</center><br />
<br />
While the lottery officials want to have higher jackpots, they also do not want too long a period between jackpots. Normally the increase in the size of the lottery, when no one wins the jackpot, is determined by the amount taken in in this unsuccessful drawing. This was recently changed so that, when a new record jackpot occurs and no-one wins it, at most 25 million dollars are added to the Jackot until someone wins the jackpot. The money save by this is added to the second prize.<br />
<br />
When the 340 million jackpot was won, 49 players had the five basic numbers correct but not the bonus numbers. For these winners the $200,000 prize had 653,492 added to their prize so they each won $853,492. If they chosen the Powerball play option for an extra $1 their $200,000 would have been multiplied by 2,3,4, or 5 with equal probabilities. Thus if Gregg had chosen the Powerball play option, and been lucky, he would have won 1,653,492 dollars that he could add to his 15 or so million dollars he has in stocks. <br />
<br />
===DISCUSSION===<br />
<br />
(1) Do you think it is fair to advertise the lottery prize as 340 million when the cash prize is only 164.4 million?<br />
<br />
(2) What is the probability of winning the second prize?<br />
<br />
(3) Assuming that the estimate 106 million for the number of tickets sold find the expected number of second prize winners.<br />
<br />
==Mammograms Validated as Key in Cancer Fight==<br />
<br />
The ''New York Times'' [http://www.nytimes.com/2005/10/27/health/27breast.html reported] on October 27, 2005 on a new National Cancer Institute study that attributed a significant decrease in the death rate from breast cancer to mammogram screening tests. The study, published in the New England Journal of Medicine, found that from 28% to 65% of the sharp 24% decrease in breast cancer death rates from 1990 to 2000 was due to screening; the remainder was attributed to new drugs used to treat the disease.<br />
<br />
Prior to this study, the value of mammogram screening had been disputed, for several reasons. In the general population, the test results in a large proportion number of false positives, about 90%. Thus, many women who are cancer-free are subjected to unnecessary procedures. Also, approximately 30% of cancers that are detected and treated would not have progressed significantly. Unfortunately, it isn't possible to distinguish between these so-called ''indolent'' cancers and those that become life-threatening, so it is routine practice to treat them all.<br />
<br />
The new study suggests that the benefits of routine mammography are more certain than earlier believed, according to Don Berry, Chairman of the biostatistics department of M. D. Anderson Cancer Center, in Houston, Texas, and the lead author of the paper. He said that the new study for the first time properly separates the effects of therapy and screening. Nonetheless, he cautioned that mammography does pose risks, and recommended that women be counselled before screening.<br />
<br />
Contributed by Bill Jefferys<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div></div>Nano12https://www.causeweb.org/wiki/chance/index.php?title=Main_Page&diff=1570Main Page2005-11-05T09:34:47Z<p>Nano12: </p>
<hr />
<div><center>[[Image:news.gif |300px]] </center><br />
*[[Chance News 9]]: Nov 1 2005 to Nov 15 2005:Under construction<br />
*[[Chance News 8]]: Oct 15 2005 to Oct 31 2005:New<br />
*[[Chance News 7]]: Oct 1 2005 to Oct 14 2005:New<br />
*[[Previous Chance News]]<br />
*[[How to submit a new article or edit an existing article]]<br />
<br />
Chance News reviews current issues in the news that use probability or statistical concepts. Its aim is to give the general public a better understanding of chance news as reported by the media and to allow teachers of probability and statistics courses to liven up their courses with current news. From 1992 to 2004, Chance News was written by a small number of regular contributors. These are archived on the [http://www.dartmouth.edu/~chance Chance Website] where you will also find other resources for teaching a probability or statistic course. <br />
<br />
Chance News is now a "Wiki". A Wiki is a web site designed to allow readers to easily add contributions or edit existing contributions. This makes it collaborative effort of its readers in the spirit of the very successful free encyclopedia [http://en.wikipedia.org/wiki/Main_Page Wikipedia]. (The word wiki is from the Hawaiian word wiki-wiki meaning quick).<br />
<br />
It is not necessary to login to read Chance News but it is necessary to login to add items or edit existing items. For this you need to create an account and login. (See the top of any page). <br />
<br />
We plan to have an issue of Chance News every month which includes items received in this time interval. We will use the Chance listserv to send out notices that a new Chance News has been completed. You can sign on or off or change your address <br />
for this listserv [http://listserv.dartmouth.edu/Archives/chance.html here]. This listserv is used only for this posting. <br />
<br />
Chance News will continue to be freely available under the [http://www.gnu.org/copyleft/fdl.html GNU Free Documentation License]<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div></div>Nano12https://www.causeweb.org/wiki/chance/index.php?title=Chance_News_7&diff=1555Chance News 72005-11-05T09:34:43Z<p>Nano12: /* Which foods prevent cancer? */</p>
<hr />
<div>Sept 26 2005 to Oct 15 2005<br />
==Quotation==<br />
<blockquote><br />
While writing my book [Stochastic Processes] I had an argument with Feller [Introuction to Probability Theory and its Applications]. He asserted that everyone said "random variable" and I asserted that everyone said "chance variable." We obviously had to use the same name in our books, so we decided the issue by a stochastic procedure. That is, we tossed for it and he won. </blockquote><br />
<br />
<p align = right> Joe Doob<br><br />
[http://www.dartmouth.edu/~chance/Doob/conversation.html Statistical Science]<br><br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Forsooth==<br />
<br />
Peter Winkler suggested our first forsooth.<br />
<br />
<blockquote>Texas beats Ohio State in their opening game <br />
of the season (Saturday Sept 10 2002). The sportscasters (legendary Brent Musburger on play-by-play or Gary Danielson on analysis) observed that of the 14 teams who have <br />
previously played in the championship game (at the end of each season) 5 <br />
have suffered an earlier defeat. "Thus," they conclude, "Ohio State can <br />
still make it to the championship game, but their chances are now less <br />
than 50%."</blockquote><br />
<br />
===Discussion===<br />
<br />
What is wrong with this?<br />
----<br />
Here are forsooths from the September 2005 issues of RSS NEWS<br />
<br />
<blockquote>'Big ticket quiz' at the start of Wimbledon:<br><br><br />
Q. How many punnets (a small light basket or other container for fruit or vegetables) of strawberries are eaten each day during the Wimbledon tournament?<br><br />
Is it (a) over 8,000, (b) over 9,000 or (c) over 10,000?</blockquote><br />
<br />
<div align="right">BBC radio 5<br><br />
20 June 2005</div><br />
<br />
<blockquote>Waiting time for foot surgery down by 500%</blockquote><br />
<br />
<div align="right">Evening News (Edinburgh)<br><br />
5 July 2005</div><br />
<br />
The next two forsooths are from the October RSS news.<br />
<br />
<blockquote>In 1996-8 when the number attending university was static, the participation of women was also static, but male participation fell.</blockquote><br />
<br />
<div align="right">The Times Higher<br><br />
21 January 2005</div><br />
<br />
<blockquote>[On the subject of congestion on the London Underground..] 'Last year 976 million of us used the tube...'</blockquote><br />
<br />
<div align="right">BBC London News<br><br />
19 May 2005</div><br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Fortune's Formula==<br />
<br />
''Fortune's Formula: Wanna Bet?''<br><br />
''New York Times Book Section'', September 25, 2005<br><br />
David Pogue<br />
<br />
This must be the kind of review that every Science writer dreams of. Pogue ends his review with:<br />
<br />
<blockquote> ''Fortune's Formula'' may be the world's first history book, gambling primer, mathematics text, economics manual, personal finance guide and joke book in a single volume. Poundstone comes across like the best college professor you ever had, someone who can turn almost any technical topic into an entertaining and zesty lecture. But every now and then, you can't help wishing there were some teaching assistants on hand to help.</blockquote><br />
<br />
The author William Poundstone is a science writer who has written a number of very successful science books. His book, ''Prisoner's dilemma: John von Neumann, game theory and the puzzle of the bomb'', was written in the style of this book. Indeed Helen Joyce, in her review of this book in Plus Magazine writes:<br />
<br />
<blockquote>This book is a curious mixture of biography, history and mathematics, all neatly packaged into an entertaining and enlightening read. </blockquote><br />
<br />
Poundstone describes himself as a visual artist who does books as a "day job.". You can learn about his art work [http://www.uiowa.edu/~iareview/tirweb/feature/poundstone/interview2.htm here].<br />
<br />
''Fortune's Formula'' is primarily the story of Edward Thorp, Claude Shannon, and John Kelly and their attempt to use mathematics to make money gambling in casinos and on the stock market. None of these did their graduate work in mathematics. Thorp and Kelly got their Phd's in physics and Shannon in Genetics. <br />
<br />
In the spring of 1955, while a graduate student at UCLA, Thorp joined a discussion on the possiblity of making money from roulette. Thorp suggested that they could taking advantage of the fact that bets are still accepted for a few second after the croupier releases the ball, and in these seconds, he could estimate what part of the wheel the ball would stop. <br />
<br />
Thorp did not pursue this and in 1959 became an instructor in mathematics at M.I.T. Here he became interested in blackjack and developed his famous card counting method for wining at blackjack. He decided to publish his method in the most prestigious journal he could find and settled on ''Proceedings of the National Academy of Sciences''. For this he needed to have a member of the Academy submit his paper. The only member in the math department was Shannon so he had to persuade him of the importance of his paper. Shannon not only agreed but in the process became fascinated by Thorp's idea for beating roulette. He agreed to help Thorp carry this out. They built a roulette machine in Shannon's basement. It worked fine there in trial runs but not so well in the casino so they did not pursue this method of getting rich. <br />
<br />
Of course Thorp is best known for showing that blackjack is a favorable game and giving a method to exploit this fact. Shannon is best known for his work in information theory. Kelly is known his method for gambling in a favorable game. This plays a central role in Poundstone's book and is probably why Pogue felt that it would help if he had a teaching assistant. Poundstone tries to explain Kelly's work in many different ways but what he really needed to understand it is an example but this required too many formulas for a popular book. So we shall include an example from Chance News 7.09. <br />
<br />
Writing for Motley Fool, 3 April 1997 Mark Brady complained about the inumeracy of the general public and gave a number of examples including this one:<br />
<br />
<blockquote> Fear of uncertainty and innumeracy are synergistic. Most people cannot do the odds. What is a better deal over a year? A 100% safe return with 5 percent interest or a 90 percent safe return with a 20 percent return. For the first deal, your return will be 5% percent. For the second, your return will be 8%. Say you invest $1000 10 times. Your interest for the 9 successful deals will be 9000 x 0.2 or 1800. Subtract the 1000 you lost on the 10th deal and you get a $800 return on your original $10,000 for 8 percent.</blockquote><br />
<br />
Peter Doyle suggested that a better investment strategy in this case is:<br />
<br />
Faced with a 100 percent-safe investment returning 5 percent and a 90 percent-safe investment returning 20%, you should invest 20% of your funds in the risky investment and 80% in the safe investment. This gives you an effective return of roughly 5.31962607969968292 percent. <br />
<br />
Peter is using a money management system due to J. L. Kelly (1956: "A new interpretation of information rate," ''Bell System Technical Journal'', '''35'''). Kelly was interested in finding a rational way to invest your money faced with one or more investment schemes, each of which has a positive expected gain. He did not think it reasonable to try simply to maximize your expected return. If you did this in the Motley Fools example as suggested by Mark Brady, you would choose the risky investment and might well lose all your money the first year. We will illustrate what Kelly did propose in terms of Motley Fools example. <br />
<br />
We start with an initial capital, which we choose for convenience to be $1, and invest a fraction r of this money in the gamble and a fraction 1-r in the sure-thing. Then for the next year we use the same fractions to invest the money that resulted from the first year's investments and continue, using the same r each year. Assume, for example, that in the first and third years we win the gamble and in the second year we lose it. Then after 3 years our investment returns an amount f(r) where: <br />
<br />
<math><br />
f(r) = (1.2r + 1.05(1-r))(1.05(1-r))(1.2r + 1.05(1-r)). <br />
</math><br />
<br />
After n years, we would have n such factors, each corresponding to a win or a loss of our risky investment. Since the order of the terms does not matter our capital will be: <br />
<br />
<math><br />
f(r,n) = (1.2r + 1.05(1-r))^W(1.05(1-r))^L<br />
</math><br />
<br />
where W is the number of times we won the risky investment and L the number of times we lost it. Now Kelly calls the quantity:<br />
<br />
<math><br />
G(r) =\lim_{n \to \infty }\frac{\log(f( r,n)} {n}<br />
</math> <br />
<br />
the exponential rate of growth of our capital. In terms of G(r) our capital should grow like <math> e^{G(r)} </math>. In our example: <br />
<br />
<math><br />
\log(\frac{f(r,n)}{n}) = \frac{W}{n}\log(1.2r + 1.05(1-r)) + \frac{L}{n}\log(1.05(1-r))<br />
</math> <br />
<br />
Since we have a 90% chance of winning our gamble, the [http://en.wikipedia.org/wiki/Strong_law_of_large_numbers#The_strong_law strong law of large numbers] tells us that as n tends to infinity this will converge to <br />
<br />
<math><br />
G(r) = 0.9\log(1.2r + 1.05(1-r))+0.1\log(1.05(1-r))<br />
</math><br />
<br />
It is a simple calculus problem to show that G(r) is maximized by r = 0.2 with: <br />
G(0.2) = 0.05183. Then e^{0.05183} = 1.0532, showing that our maximum rate of growth is 5.32% as claimed by Peter. <br />
<br />
The attractiveness of the Kelly investment scheme is that, in the long run, any other investment strategy (including those where you are allowed to change your investment proportions at different times) will do less well. "In the long run and less well" means more precisely that the ratio of your return under the Kelly scheme and your return under any other strategy will tend to infinity.<br />
<br />
Thorp had a very good experience in the stock market, which is described very well by Gaeton Lion in his excellent [http://www.amazon.com/gp/product/customer-reviews/0809046377/ref=cm_cr_dp_pt/103-8647004-5865443?%5Fencoding=UTF8&n=283155&s=books review] of ''Fortune's Formula''. He writes:<br />
<br />
<blockquote> Ed Thorp succeeded in deriving superior returns in both gambling and investing. But, it was not so much because of Kelly's formula. He developed other tools to achieve superior returns. In gambling, Ed Thorp succeeded at Black Jack by developing the card counting method. He just used intuitively Kelly's formula to increase his bets whenever the odds were in his favor. Later, he ran a hedge fund for 20 years until the late 80s and earned a rate of return of 14% handily beating the market's 8% during the period. <br><br><br />
<br />
Also, his hedge fund hardly lost any value on black Monday in October 1987, when the market crashed by 22%. The volatility of his returns was far lower than the market. He did this by exploiting market inefficiencies using warrants, options, and convertible bonds. The Kelly formula was for him a risk management discipline and not a direct source of excess return. </blockquote><br />
<br />
Shannon also made a lot of money on the stock market, but did not use Kelly's formula. In his [http://www.amazon.com/gp/product/customer-reviews/0809046377/ref=cm_cr_dp_pt/103-8647004-5865443?%5Fencoding=UTF8&n=283155&s=books review] Gaeton Lion writes<br />
<br />
<blockquote>Claude Shannon amassed large wealth by recording one of the best investment records. His performance had little to do with Kelly's formula. Between 1966 and 1986, his record beat even Warren Buffet (28% to 27% respectively). Shannon strategy was similar to Buffet. Both their stock portfolios were concentrated, and held for the long term. Shannon achieved his record by holding mainly three stocks (Teledyne, Motorola, and HP). The difference between the two was that Shannon invested in technology because he understood it well, while Buffet did not. </blockquote><br />
<br />
Finally, Thorp provided the following comments for the book cover:<br />
<br />
<blockquote>From bookies to billionaires, you'll meet a motley cast of characters in this highly original, 'outside the box' look at gambling and investing. Read it for the stories alone, and you'll be surprised at how much else you can learn without even trying. --Edward O. Thorp, author of ''Beat the Dealer'' and ''Beat the Market''.</blockquote><br />
<br />
Submitted by Laurie Snell.<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Which foods prevent cancer?==<br />
<br />
Which of these foods will stop cancer? (Not so fast)<br><br />
New York Times, 27 September 2005, Sect. F, p. 1<Br><br />
Gina Kolata<br />
<br />
Among other examples, the article includes a [http://www.nytimes.com/imagepages/2005/09/26/science/20050927_CANCER_GRAPHIC.html data graphic] on purported benefits of dietary fiber in preventing colorectal cancer. Early observational studies indicated an association, but subsequent randomized experiments found no effect. <br />
<br />
More to follow.<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Slices of risk and the <em>broken heart</em> concept==<br />
[http://www.gloriamundi.org/picsresources/news20050912.pdf How a Formula Ignited Market That Burned Some Big Investors],<br />
Mark Whitehouse, The Wall Street Journal, September 12, 2005.<br><br />
<br />
This on-line article relates how a statistician, David Li,<br />
unknown outside a small coterie of finance theorists, helped change the world of investing. <br />
<br />
The article focuses on a event last May when General Motors Corp's debt<br />
was downgraded to junk status, causing turmoil in some financial markets.<br />
The article gives a nice summary of the underlying financial instruments known<br />
as credit derivatives -<br />
investment contracts structured so their value depends on the behavior of some other thing or event -<br />
with exotic names like <br />
[http://en.wikipedia.org/wiki/Collateralized_debt_obligations collateralized debt obligations] and [http://en.wikipedia.org/wiki/Credit_default_swap credit-default swaps].<br />
<br />
The critical step is to estimate the likelihood that many of the companies <br />
in a pool of companies would go bust at once. <br />
For instance, if the companies were all in closely related industries,<br />
such as auto-parts suppliers, they might fall like dominoes after a catastrophic event.<br />
Such a pool would have a 'high default correlation'.<br />
<br />
In 1997, nobody knew how to calculate default correlations with any precision. <br />
Mr. Li's solution drew inspiration from a concept in actuarial science known as the <br />
<em>broken heart</em> syndrome - people tend to die faster after the death of a beloved spouse. <br />
Some of his colleagues from academia were working on a way to predict this<br />
death correlation, something quite useful to companies that sell life insurance and joint annuities.<br />
He says:<br />
<blockquote><br />
Suddenly I thought that the problem I was trying to solve was exactly like the problem these<br />
guys were trying to solve,.<br />
Default is like the death of a company, so we should<br />
model this the same way we model human life."<br />
</blockquote><br />
<br />
This gave him the idea of using [http://en.wikipedia.org/wiki/Copula_%28statistics%29 copulas], <br />
mathematical functions the colleagues had begun applying to actuarial science. <br />
Copulas help predict the likelihood of various events<br />
occurring when those events depend to some extent on one another. <br />
Until the events last May of this year, one of the most popular copulas for bond pools <br />
was the Gaussian copula, named after <br />
[http://en.wikipedia.org/wiki/Carl_Friedrich_Gauss Carl Friedrich Gauss], a 19th-century German statistician. <br />
<br />
===Further reading===<br />
* The [http://www.gloriamundi.org/picsresources/news20050912.pdf on-line article] gives more details about what went wrong in the financial markets in May and the search for a more appropriate copula to capture better the <em>broken heart</em> syndrome between companies.<br />
* [http://en.wikipedia.org/wiki/Wikipedia Wikipedia] is a very worthwhile on-line resource for definitions of technical words, such as [http://en.wikipedia.org/wiki/Copula_%28statistics%29 copula].<br />
<br />
Submitted by John Gavin.<br />
<br />
<br />
==Learning to speak via statistics and graph theory==<br />
<br />
[http://education.guardian.co.uk/tefl/teaching/story/0,15085,1576100,00.html Computer learns grammar by crunching sentences], Max de Lotbinière September 23, 2005, [http://www.guardianweekly.co.uk/ Guardian Weekly].<br><br />
[http://www.cornellsun.com/vnews/display.v/ART/2005/09/09/432118a84f6af Profs’ New Software ‘Learns’ Languages], Ben Birnbaum, 9 Sep 2005, Cornell Daily Sun.<br />
<br />
A language-learning robot may sound like science fiction but new software, developed by Cornell University psychology professor Shimon Edelman, with colleagues Zach Solan, David Horn and Eytan Ruppin from Tel Aviv University in Israel, is well on the way to constructing a computer program that can teach itself languages and make up its own sentences, the developers' claim.<br />
<br />
Unlike previous attempts at developing computer algorithms for language learning - "Automatic Distillation of Structure," or "ADIOS" for short - discovers complex patterns in raw text by repeatedly aligning sentences and looking for overlapping parts.<br />
Once it has derived a language's rules of grammar,<br />
it can then produce sentences of its own, simply from blocks of text in that language.<br />
<br />
It has been evaluated on artificial context-free grammars with thousands of rules, <br />
on natural languages as diverse as English and Chinese, <br />
on coding regions in DNA sequences and on protein data correlating sequence with function. <br />
<br />
Edelman comments:<br />
<blockquote><br />
Adios relies on a statistical method for pattern extraction and on structured generalisations <br />
- the two processes that have been implicated in language acquisition.<br />
Our experiments show that Adios can acquire intricate structures <br />
from raw data including transcripts of parents' speech directed at two- or three-year-olds.<br />
This may eventually help researchers understand how children, <br />
who learn language in a similar item-by-item fashion, and with little supervision, <br />
eventually master the full complexity of their native tongue.<br />
</blockquote><br />
<br />
[http://plus.maths.org/latestnews/may-aug05/adios/ Plus Magazine's website]<br />
offers a more logical explanation:<br />
<blockquote><br />
The ADIOS algorithm is based on statistical and algebraic methods performed on one of the most basic and versatile objects of mathematics - the graph.<br />
Given a text, the program loads it as a graph by representing each word by a node, or vertex, and each sentence by a sequence of nodes connected by lines. A string of words in the text is now represented by a path in the graph. <br><br />
<br />
Next it performs a statistical analysis to see which paths, or strings of words, occur unusually often. <br />
It then decides that those that appear most frequently - called "significant patterns" - <br />
can safely be regarded as a single unit<br />
and replaces the set of vertices in each of these patterns by a single vertex, <br />
thus creating a new, generalised, graph.<br><br />
<br />
Finally, the program looks for paths in the graph which just differ by one vertex. <br />
These stand for parts of sentences that just differ by one word (or compound of words) like "the cat is hungry" and "the dog is hungry". <br />
Performing another statistical test on the frequency of these paths, the program identifies classes of vertices, or words, that can be regarded as interchangeable, or equivalent. <br />
The sentence involved is legitimate no matter which of the words in the class - in our example "cat" or "dog" - you put in.<br><br />
<br />
This last step is then repeated recursively.<br><br />
</blockquote><br />
<br />
[http://plus.maths.org/latestnews/may-aug05/adios/ The website] uses graphs to illustrate some examples and it finishes with some reassuring words:<br />
<blockquote><br />
All this doesn't mean, of course, that the program actually "understands" what it's saying. It simply knows how to have a good go at piecing together fragments of sentences it has identified, in the hope that they are grammatically correct. So if, like me, you're prone to swearing at your computer, you can safely continue to do so: it won't answer back for a long while yet.<br />
</blockquote><br />
<br />
===Further reading===<br />
The [http://adios.tau.ac.il/ ADIOS homepage] offers an overview and more detailed description of the program.<br />
<br />
Submitted by John Gavin.<br />
<br />
==Understanding probability==<br />
<br />
Understanding Probability:Chance rules in everyday life<br><br />
Cambridge University Press 2004<br><br />
Henk Tijms<br />
<br />
Hank Tijms is Professor in Operation Research at the Vrije University in Amsterdam. This book is based on his earlier Dutch book “Spelen met Kansen.” <br />
<br />
The aim of this book is to show how probability applies to our everyday life in a way that your Uncle George could understand even if he has forgotten much of his high school math. Tijms does not try to avoid mathematics but only to postpone the formal math until the reader has seen the many applications of probability in the real world, how much fun it is, and learned to work problems and when he can’t work one how to get the answer by simulation. He learns all this in part I of the book and then he learns the more formal math in Part II.<br />
<br />
In Chapter 1 Tijms asks the reader to think about problems with surprising answers in the spirit of Susan Holmes “[http://www-stat.stanford.edu/~susan/surprise/ Probability by Surprise]” including the birthday problem and the Monty Hall problem. Readers are on their own to try to solve one or more of the problems but promised that they will see the solutions later in the book. <br />
<br />
Chapter 2 deals with the law of large numbers and introduces the concept of simulation. This theorem is explained and illustrated by problems related, for example, to coin tossing, random walks and casino games. Expected value is introduced in an informal way to be defined more carefully later in the book. For the reader who is not frightened by mathematical formulas, Tijms includes a discussion of the Kelly betting system with a footnote saying that this paragraph can be skipped at first reading. This is a fascinating topic that is widely applied in gambling and stock investment but rarely appears in a probability book.<br />
<br />
In Chapter 3 the author returns to previous problems such as the birthday problem and gambling systems and solves them first by simulation and then by mathematics. <br />
<br />
In this chapter Tijms describes Efron’s bootstrap method and uses it to solve a number of problems including a hypothetical clinical trial and to test if the famous 1970 draft lottery during the Vietnam War was fair. Again the bootstrap method has wide application but rarely occurs in an elementary probability or statistics book.<br />
<br />
Chapter 4 describes the binomial, Poisson, and hypergeomtric distributions and how to use them in solving problems such as the famous hat check problem, and a variety of interesting lottery questions. The Poisson process is discussed but again with the footnote that novice readers might want to read this at a later time.<br />
<br />
Chapter 5 is mainly about Center Limit Theorem and its many applications especially to statistics. <br />
<br />
Chapter 6 introduces Chance trees and Bayes’s rule. The tree method is used to explain a variety of problems including the Monty Hall Problem and the false-positive paradox. <br />
<br />
This is a brief description of the first six chapters which constitute Part I of the book. Now the fun is over. Part 2 called “Essentials of probability” looks like the traditional first chapters in a standard probability book. But the reader has already found how exciting probability is, has a good intuitive idea of the basic concepts and has worked many of the interesting problems at the end of each chapter either using math or simulation. For some students this might allow them to actually enjoy Part 2. But your Uncle George may want to quit while they are ahead. <br />
<br />
Tijms writes with great clarity and his enthusiasm for probability in the real world is contagious. We were delighted to see, as acknowledged in the preface, that Tijms included several of the more interesting problems discussed in Chance News, often going well beyond what we had said in our discussion of the problem. <br />
<br />
This book presents a completely new way to go about teaching a first course in probability and we think those who teach such a course should consider trying it out.<br />
<br />
===Discussion===<br />
<br />
(1) In the days of Basic we required all students to learn Basic in their first math course so we could assume that students could write programs to simulate probability problems and so me made heavy use of simulation as suggested in this book. The author uses Pascal in his book. What present language do you think is easiest for a student with no computing experience to learn?<br />
<br />
We asked Professor Tijms what the situation was in math departments in Europe and he replied:<br />
<br />
<blockquote>In math departments of universities and polytechnic schools in Europe students learn to write computer programs. In my university they still learn to program in Java and C++ ( in previous days Pascal), but I see in the Netherlands the trend that the instructors think it is sufficient if the students are able to program in Matlab. <br><br><br />
<br />
In ny book I have chosen to formulate the simulation programs in Pascal because of the clarity and the simplicity of the language, though this language is hardly used anymore. The introductory probability course at my university is given before they have learned to program, but this does not prevent them of simulating probability problems by using Excel. In the simulation of many elementary probability problems a random-number generator alone suffices to simulate those problems and so Excel can be used. In the second year they have mastered Matlab, a perfect tool with its excellent graphics to simulate many challenging probability problems ( they really like it, in particular when it concerns problems such as the problems 2.24-2.45 in chapter 2 and the problems 5.11-5.13 in chapter 5). <br />
</blockquote><br />
<br />
<br />
(2) Do you think that probability books should include data to test probability models that are said to describe real world problems? If so name some models that you think would pass such a test and some that you think might not.<br />
<br />
Submitted by Laurie Snell<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Societies worse off when they have God on their side==<br />
<br />
[http://www.timesonline.co.uk/article/0,,2-1798944,00.html Societies worse off when they have God on their side]<br><br />
Timesonline, September 27, 2005<br><br />
Ruth Gledhill<br />
<br />
[http://moses.creighton.edu/JRS/2005/2005-11.html Cross-national correlations of quantifiable societal health with popular religiosity and secularism in the prosperous democracies]<br><br />
Journal of Religion & Society, Vol.7(2005)<br><br />
Gregory S. Paul<br />
<br />
In the Times article we read:<br />
<br />
<blockquote>According to the study, belief in and worship of God are not only unnecessary for a healthy society but may actually contribute to social problems.<br><br><br />
Many liberal Christians and believers of other faiths hold that religious belief is socially beneficial, believing that it helps to lower rates of violent crime, murder, suicide, sexual promiscuity and abortion. The benefits of religious belief to a society have been described as its “spiritual capital”. But the study claims that the devotion of many in the US may actually contribute to its ills. <br />
</blockquote><br />
<br />
Gregory Paul is a dinosaur paleontologist and on an [http://www.abc.net.au/worldtoday/indexes/2005/twt_20050928.htm interview] on Australian ABC radio Paul said that, being a paleontologist, for many years he had to deal with the issue of creationism versus evolutionary science in the U.S and his interest in evolutionary science prompted him to look at whether there was any link between the religiosity of a society and how well that society functions. <br />
<br />
If you look at Paul's article you will find very little technical statistical analysis, for example, he did not carry out a regression analysis. Rather he rests his case on the series of scatterplots.<br />
<br />
Paul describes his data sources as:<br />
<br />
<blockquote>Data sources for rates of religious belief and practice as well as acceptance of evolution are the 1993 Environment I (Bishop) and 1998 Religion II polls conducted by the International Social Survey Program (ISSP), a cross-national collaboration on social science surveys using standard methodologies that currently involves 38 nations. The last survey interviewed approximately 23,000 people in almost all (17) of the developed democracies; Portugal is also plotted as an example of a second world European democracy. Results for western and eastern Germany are combined following the regions' populations. England is generally Great Britain excluding Northern Ireland; Holland is all of the Netherlands. The results largely agree with national surveys on the same subjects; for example, both ISSP and Gallup indicate that absolute plus less certain believers in a higher power are about 90% of the U.S. population. The plots include Bible literalism and frequency of prayer and service attendance, as well as absolute belief in a creator, in order to examine religiosity in terms of ardency, conservatism, and activities. </blockquote><br />
<br />
Here are the countries Paul considered with the abbreviations used on the graphics. <br />
<br />
A = Australia, C = Canada, D = Denmark, E = Great Britain, F = France, G = Germany,<br />
H = Holland, I = Ireland, J = Japan, L = Switzerland, N = Norway, P = Portugal, R = Austria,<br />
S = Spain, T = Italy, U = United States, W = Sweden, Z = New Zealand.<br />
<br />
There seems to be no agreement as to which countries are developed democracies. For example Paul might have included Greece and Belgium, Finland, and others but the data may have determined his choice. Paul comments that he added Portugal as an example of a second world democracy. <br />
<br />
Paul's anaysis of the data includes a series of 9 Figures which are available at the end of the article and are the most interesting part of the study. If you try printing Paul's article you will only get the first of his 9 Figures. When you look at the [http://moses.creighton.edu/JRS/2005/2005-11.html web version] you will still see only Figure 1 but the others can be viewed by selecting the numbers from 2 to 9 on the left side of Figure 1.<br />
<br />
Figure 1 deals with the proportion of people who accept human evolution which is interesting but not as relevant to the welfare of the people as others so we will look at Figure 2.<br />
<br />
[[Image:religion2.png|500px|center|Source:Gregory Paul]]<br />
<br />
Each Figure iprovides 5 separate scatterplots. Ïn Figure 2 we see that the U.S. has largest number--between 6 and 7-- of homicides per 100,000 and Spain has the lowest number with less than 1 homicide per 100,000. We also see that the U.S. has the highest proportion of people, about 25%, who take the bible literally while several countries have less than 10% such people.<br />
<br />
What we cannot do is compare the number of homicides per thousand between those who take the bible literally and those who are agnostics or atheists which is what we would really want to know. Presumably the data did not permit this comparison. <br />
<br />
[[Image:religion3.png|500px|center|Source:Gregory Paul]]<br />
<br />
Figure 3 deals with "14-24 year old suicides per 100,000". Here the U.S. is in about the middle.<br />
<br />
Figure 4 deals with the "under-five mortalities per 1000 births".<br />
<br />
[[Image:religion4.png|500px|center|Source:Gregory Paul]]<br />
<br />
Ignoring Portugal, the U.S. has the highest number of under-five mortalities per 1000 births-- between 7 and--8 while several countries have only 4.<br />
<br />
The other figures can be seen at end of Paul's article. They deal with life expectancy, sexually transmitted diseases, abortion and 15-16 year old pregnancies. Life expectancy is the smallest in the U.S. and for sexually transmitted diseases, abortion and 15-17 year old prenacies the U.S. is at the top of the graphs and in fact these look like outliers.<br />
<br />
Well, this study does not by itself justify the Times hedline: "Societies worse off when they have God on their side." Paul himself would not claim this. He writes:<br />
<br />
<blockquote> This study is a first, brief look at an important subject that has been almost entirely neglected by social scientists. The primary intent is to present basic correlations of the elemental data. Some conclusions that can be gleaned from the plots are outlined. This is not an attempt to present a definitive study that establishes cause versus effect between religiosity, secularism and societal health. It is hoped that these original correlations and results will spark future research and debate on the issue.</block<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div></div>Nano12https://www.causeweb.org/wiki/chance/index.php?title=Chance_News_9&diff=1554Chance News 92005-11-05T09:34:40Z<p>Nano12: /* Supreme Court Nominee Alito: Statistics Misleading? */</p>
<hr />
<div>==Quotation==<br />
Å quotation will be added here.<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Forsooth==<br />
Forsooth items should be added here.<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Supreme Court Nominee Alito: Statistics Misleading?==<br />
An [http://www.salon.com/politics/war_room/2005/10/31/jury/index.html article] in Salon.com for October 31 discusses the first-degree murder trial, Riley v. Taylor. The defendant Riley was African-American; at the trial, the prosecution used its peremptory challenges to eliminate all three of the African-Americans on the jury panel. In the same county that year, there were three other first-degree murder trials, and in every one of those cases all of the African-American jurors were struck.<br />
<br />
A majority of the judges on the appeals court thought that there was evidence that jurors were struck for racial reasons. According to them, a simple calculation indicates that there should have been five African-American jurors amongst the forty-eight that were empanelled. However, there were none. To these judges, this was clear evidence of racial motivaion in the striking of such jurors.<br />
<br />
Judge Alito dissented. He called the majority's analysis simplistic, and stated that although only 10% of the U.S. population is left-handed, five of the last six people elected president of the United States were left-handed. He asked rhetorically whether this indicated bias against right-handers amongst the U.S. electorate.<br />
<br />
The majority responded that there is no provision in the Constitution that protects persons from discrimination based on whether they are right-handed or left-handed, and that to compare these cases with the handedness of presidents ignores the history of racial discrimination in the United States.<br />
<br />
===Questions===<br />
<br />
1) Assuming that Judge Alito is correct about the proportion of left-handers in the U.S. population, what is the probability that five of the last six presidents elected would be left-handed?<br />
<br />
2) Is Judge Alito's comparison biased by the fact that he chose just the last six presidents? Presumably he believed that the president just before this group was right-handed, otherwise he would have included him in the sample and said "six of the last seven presidents." What is the relevant statistic?<br />
<br />
3) When the decision came down in 2001, the last six people elected president were George W. Bush, Clinton, George H. W. Bush, Reagan, Carter and Nixon. Of these, Clinton and George H. W. Bush were left-handed. Ford, who was left-handed, was not elected president (or even vice-president); he became president upon the resignation of Richard Nixon. Reagan may have been left-handed as a child, but he wrote right-handed so his case isn't clear; the Reagan Presidential Library [http://www.reagan.utexas.edu/archives/reference/facts.html says] that he was "generally right-handed." Judge Alito may have been confused, including on his list Ford (who was not elected) and George W. Bush (who is not left-handed, although his father is), as well as Reagan. The other left-handed presidents were Truman and Garfield. Hoover is found on some lists of left-handed presidents, but according to the Hoover Institution, he was not left-handed. How does this information affect Alito's argument?<br />
<br />
4) Suppose that 5/48 of the jury pool were African-American. What is the probability that no juror amongst the 48 selected would have been African-American? How does this compare with the actual statistics of left-handed presidents? Does the same objection apply to this case as might apply to Alito's example?<br />
<br />
5) What is your opinion? Is there clear statistical evidence of racial bias in the use of peremptory challenges in this county?<br />
<br />
6) What does it say about our judiciary that Judge Alito could get his facts as wrong as he did, and that none of the judges in the majority caught the errors?<br />
<br />
Contributed by Bill Jefferys<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==item2==<br />
Replace item2 by the name of your article.</div>Nano12https://www.causeweb.org/wiki/chance/index.php?title=Chance_News_8&diff=1553Chance News 82005-11-05T09:34:36Z<p>Nano12: /* DISCUSSION */</p>
<hr />
<div>Oct 15 to Oct 30<br />
<br />
==Quotation==<br />
<blockquote>One more fagot of these adamantine bandages, is, the new science of Statistics. It is a rule, that the most casual and extraordinary events -- if the basis of population is broad enough -- become matter of fixed calculation. It would not be safe to say when a captain like Bonaparte, a singer like Jenny Lind, or a navigator like Bowditch, would be born in Boston: but, on a population of twenty or two hundred millions, something like accuracy may be had. Ralph Waldo Emerson Fate</blockquote><br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Forsooth==<br />
Here's another Forsooth from the October issue of RSS News.<br />
<blockquote>Your'e more likely to die in a fire in Strathclyde than anywhere else in the country</blockquote><br />
<br />
<div align="right">BBC1 mews bullietin<br><br />
11 May 2005</div><br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==The Poisson distribution and the Supreme Court==<br />
The Poisson distribution and the Supreme Court<br><br />
''Journal of the American Statistical Association'' 31, no. 195 ,(1936), 376-80<br><br />
W. Allen Wallis<br />
<br />
Supreme Court Appointments as a Poisson distribution<br><br />
''American Journal of Political Science'', 26, No.1, February 1982<br><br />
S. Sidney Ulmer<br />
<br />
This is not current news, but since Supreme Court appointments are in the news we felt that these articles might make an interesting class discussion.<br />
<br />
In 1936 statistician Allen Wallis suggested that a Poisson distribution can approximate the number of U.S. Supreme Court appointments in a given year. In his Table 1 Wallis provided the number appointed in each year over the intervals with different numbers of Justices on the Supreme Court: 1790-1806 (6) 1807-1836 (7), and 1837-1932 (9). Actually there were 10 in the years 1963 to 1967 which Wallis called "negligible exceptions."<br />
<br />
[[Image:wallis1.png|500px|center]]<br />
<br />
Wallis then restricts himself to the years 1837-1932 and finds that a Poisson distribution with mean .5 can approximate the number of court appointments in a year. His results are shown in his Figure II:<br />
<br />
[[Image:wallis2.png|500px|center]]<br />
<br />
In his article, Sidney Ulmer updated the data to 1980 and also includes data from the early Supreme Courts with 6 and 7 members. Thus his data covers the years 1790--1980. His Table 1 compares the actual number of appointments in a year with the expected number of appointments assuming a Poisson distribution with mean 5.13.<br />
<br />
[[Image:ulmer1.png|500px|center]]<br />
<br />
In his Table II Ulmer limits the data to the 9 member Supreme Courts: 1837 to 1862 and 1869-1980).<br />
<br />
[[Image:ulmer2.png|500px|center]]<br />
<br />
Testing the goodness of fits, Ulmer argues that the fit with the varying size Supreme Courts is just as good as with fixed size Supreme Courts.<br />
<br />
===DISCUSSION===<br />
<br />
(1) What is the probability that a President will make 2 or more appointments to the Supreme Court during a 4-year term? What is the probability a President makes no appointments during a 4-year term? Has this ever happened?<br />
<br />
(2) Do you agree with Ulmer that there is no reason to limit the data to years with the Supreme Court is the same size?<br />
<br />
(3) Obtain the data needed to update Ulmer's results to today and provide Tables that correspond to Ulmer's Tables 1 and 2. Add your Tables to this Chance News and make your data available to make it easier to update this in future years.<br />
<br />
Contributed by Laurie Snell<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Possible Cancer Cluster in Connecticut==<br />
Pratt Agrees to Increase Funding for Brain Cancer Study <br><br />
''The Associated Press''<br><br />
October 11, 2005<br><br />
Stephen Singer<br><br />
<br />
<br />
In a case that seems eerily familiar to the leukemia cancer cluster made famous by the book and movie, ''A Civil Action'', researchers are trying to determine whether or not a cancer cluster exists among workers at Pratt & Whitney, a company that manufactures jet engines. Over one hundred former or current Pratt & Whitney employees have been identified as having a relatively rare type of fatal brain tumor known as glioblastoma multiforme, which strikes 3 people per 100,000 every year. Many of these workers have been exposed to metals and chemical substances, including TCE (trichloroethylene), which is an engine degreaser. TCE is the same carcinogenic chemical that was dumped in the 1960’s and 1970’s by the chemical company, WR Grace, in Woburn, MA, and that was found to have contaminated the drinking water in two of the town’s wells. <br><br />
<br />
<br />
Prior to the recent announcement that the funding is being increased from $6 million dollars to $12 million dollars, this medical study was already being described as the largest occupational health study ever conducted. It covers 250,000 people who worked at any of the seven Connecticut Pratt & Whitney plants from 1952 to 2001. So far, at least 125 cases of brain cancer have been documented, according to the lawyer who represents dozens of individuals and family members.<br><br />
<br />
<br />
The study falls under the auspices of the Connecticut Department of Public Health. However, due to the overwhelming cost and scope of the study, Pratt & Whitney is funding the project. Since Pratt is paying for the study, they chose the researchers, a team from the University of Pittsburgh. The project began three years ago, and the results are expected to be available between 2007 and 2009.<br><br />
<br />
<br />
In the meantime, this case faces many of the obstacles common in the quest to establish whether or not a cancer cluster exists, such as proving causation, the fact that it can take a long time (sometimes 5-40 years) after exposure for true problems to show up, and finding the people who were exposed & convincing them to participate in the study. Additionally, there are legal difficulties for the families involved, including Connecticut’s statute of limitations laws, the length of time it takes investigators to reach a conclusion, the cost of litigation, and the “deep pockets” of a company like Pratt & Whitney.<br><br />
<br />
<br />
This case study provides a current example of an ongoing investigation into a possible cancer cluster. Will it ultimately be found to be a coincidence cluster or proven to be a true cancer cluster? Does it make sense that the researchers are including in the study everyone who worked at Pratt over a fifty year period, even those who only worked there for a brief time period and those who were not directly exposed to toxic substances (i.e. office workers)? Could the researchers possibly have an unconscious bias in favor of the company that is funding their research? If the company doesn’t fund the research, then who should? Is there some other way to structure such investigations, so that the company involved pays for the study, but is not allowed to choose the researchers and directly fund them?<br><br />
<br />
<br />
'''Further Reading'''<br><br />
<br />
• “Rare Cancer Found in Workers”, ''The New York Times'', March 10, 2002, Jane Gordon<br><br />
• “Scientist: Pratt Commits to Cancer Study”, ''The Hartford Courant'', May 19, 2005<br><br />
• “Participation in Cancer Study at Pratt Lagging”, ''The Hartford Courant'', October 12, 2005, Paul Marks<br><br />
• ''The New Haven Advocate'' has had more than a dozen articles that explain the working conditions at Pratt & Whitney, and also chronicle the history & progression of this case. These articles have been investigated and written primarily by Carole Bass, Associate Editor. A few of the articles are listed below. <br> <br />
-“Worked to Death”, August 2, 2001, Carole Bass & Camille Jackson<br><br />
-“Talking Cure”, October 28, 2004, Dave Goldberg<br><br />
-“Time’s Not on Their Side”, January 20, 2005, Carole Bass<br><br />
-“The Brains Behind the Brain”, October 20, 2005, Carole Bass <br><br />
For the early New Haven Advocate articles (i.e., 2001-2002) on this subject, go to http://old.newhavenadvocate.com/workedtodeath/index.html<br> <br />
For the articles since 2002, go to <br><br />
http://www.newhavenadvocate.com and search for Pratt & Whitney.<br><br />
<br />
Submitted by Josephine Rodriguez.<br />
<br />
==A record powerball lottery jackpot==<br />
<br />
On Saturday Oct 22, 2005 the powerball lottery had a record powerball jackpot of 340 million dollars. <br />
<br />
When you buy a ticket for this lottery, you specify five distinct numbers from 1 to 55, which we call basic numbers and one number from 1 to 42 called the bonus number. To win the Jackpot your 5 basic numbers and your bonus number must agree with a random choice of 5 basic numbers and one bonus number chosen by the lottery officials. The number of possible tickets is:<br />
<br />
<center><math>{55 \choose 5} 42 = </math> 146,107,962</center><br />
<br />
Thus if you buy a single ticket, the probability of having a winning jackpot ticket is<br />
<br />
<center> <math>{1} \over {146107962}</math> = .000000006844...</center><br />
<br />
The powerball website and the media expresses this by saying that the odds that you have a winning jackpot ticket is 1 in 146,107,962. <br />
<br />
Whenever there is a record jackpot, the news writers look for suggestions for other rare events that might be more familiar to its readers. <br />
<br />
Our own favorite was suggested by Fred Hoppe: if you toss a coin 27 times your chance of getting 27 heads in a row is greater than your chance of having a winning jackpot ticket when you buy a single ticket. (<math> 2^{27} = 134217728</math> and so there are 134,217,728 possible sequences of heads and tails and only 1 has all heads.)<br />
<br />
In an article for the ''Omaha World-Herald'' Oct 18, 2005 , Robynn Tysver writes:<br />
<br />
<blockquote> You have a greater chance of getting killed by lightning than winning this week's 340 million Powerball jackpot. You also have a greater chance of drowning in a bathtub. The lifetime odds of getting killed by lightning are one in 56,439, and the lifetime odds of dying while in or falling into a bathtub are one in 10,582, according to the National Safety Council. <br />
</blockquote><br />
<br />
These are not even in the ballpark. The ''Minneapolis Star Tribune'' consulted mathematicians David Bressoud and Douglas Arnold who contributed the following:<br />
<br />
According to Arnold you have a seven times better chance of becoming a saint. And Bressoud notes that you're six times more likely to get elected president of the United States. But they also provide the following more interesting estimates:<br />
<br />
<blockquote>Bressoud: "If you buy 10 tickets a week, every week, it would take you 280,000 years before you could expect to win."<br><br><br />
<br />
Arnold: "If you were to select a group of Powerball numbers every minute for 138 years, you would have about a 50 percent chance of picking the winning Powerball ticket." <br><br><br />
<br />
It is not clear what Bressoud means by "expect to win". We can check this by a simple calculation (simple for Mathematica). Let q(n) be the probability that you if you buy n tickets you fail to get a winning jackpot ticket . Then:<br />
<br />
<center> <math> \left(\frac{146107961}{146107962}\right) ^n = q(n) </math></center><br />
<br />
The average number of weeks in a year is 52.177457 so If you buy 10 tickets a week, every week for 280,000 years you will buy about 146,097,000 tickets. Using this number for n in our formula we find that you have about a 37% chance of not getting a winning lottery ticket or a 63% chance of getting one. We would not "expect to win" with a 63% chance of winning but others may. Using our formula for q(n) we find that if we buy 10 tickets a week, every week for 830,000 years you will have about a 95% chance of getting at least one winning lottery ticket which seems to us more appropriate for expecting to win. <br />
<br />
Consider now Arnold's example. Our colleague Dana Williams found that you need to buy a ticket for about 101 million lottery offerings to have about a 50% chance of getting at least one winning lottery ticket. There are an average of 525,946.766 minutes in a year. Dividing 101 million by this number gives 192.035. Thus Arnold's 138 years should be 192 years.<br />
<br />
We asked Professor Arnold about this and he replied:<br />
<br />
<blockquote> That number, which was quoted in the ''Star Tribune'' was an off-the-top-of-my-head calculation made when the reporter called me on<br />
the phone with no warning. Right ballpark, but not very accurate. Later I redid the calculation carefully.</blockquote><br />
<br />
Arnold's computations were similar to ours but he used a greater accuracy for the number of independent lotteries you have to buy to have a 50% chance of choosing the jackpot numbers at least once. His answer to this was 101,274,322. Using this, Arnold's estimate for the number of years, buying a ticket every minute, to have a 50% chance of winning a jackpot is193 years instead of our estimate of 192 years.<br />
<br />
Arnold said that he also estimated the expected value of a $1 ticket. To do this he needed an estimate for the number of tickets sold. He was told that a reasonable estimate was 106 million. In calculating the expected value of a $1 ticket he used the cash value of 164.4 million dollars instead of the annuity payout of 340 million dollars. He also took into account the possibility of having to share the jackpot. Doing this he got an expected value of exactly $1, just the price of the ticket. He commented that if he took into account the taxes the expected value would be more like 80 cents making even this lottery an unfavorable event.<br />
<br />
The news writers also gave a lot of coverage of Senator Gregg (Chairman of the Senate Budget Committee) winning $853,492 for getting the second highest prize: getting the 5 basic numbers correct but note the bonus number. Normally the prize for getting this is $200,000 cash but Gregg was the beneficiary of recent change in the powerball lottery. <br />
<br />
The powerball officials have found that increasing the size of the jackpot can increase the ticket sales because of the public's interest in large jackpots. They do this by increasing the number of possible basic numbers. When they started in 1992, to get the jackpot you had to get the 5 basic numbers chosen from 45 numbers and the 1 bonus number chosen from 45 number correct. Here are the changes so far<br />
<br />
<center><br />
1992 5 of 45 1 of 45<br><br />
1997 5 or 49 1 of 42<br><br />
2002 5 of 55 1 of 42<br><br />
2005 5 of 55 1 of 42<br><br />
</center><br />
<br />
While the lottery officials want to have higher jackpots, they also do not want too long a period between jackpots. Normally the increase in the size of the lottery, when no one wins the jackpot, is determined by the amount taken in in this unsuccessful drawing. This was recently changed so that, when a new record jackpot occurs and no-one wins it, at most 25 million dollars are added to the Jackot until someone wins the jackpot. The money save by this is added to the second prize.<br />
<br />
When the 340 million jackpot was won, 49 players had the five basic numbers correct but not the bonus numbers. For these winners the $200,000 prize had 653,492 added to their prize so they each won $853,492. If they chosen the Powerball play option for an extra $1 their $200,000 would have been multiplied by 2,3,4, or 5 with equal probabilities. Thus if Gregg had chosen the Powerball play option, and been lucky, he would have won 1,653,492 dollars that he could add to his 15 or so million dollars he has in stocks. <br />
<br />
===DISCUSSION===<br />
<br />
(1) Do you think it is fair to advertise the lottery prize as 340 million when the cash prize is only 164.4 million?<br />
<br />
(2) What is the probability of winning the second prize?<br />
<br />
(3) Assuming that the estimate 106 million for the number of tickets sold find the expected number of second prize winners.<br />
<br />
==Mammograms Validated as Key in Cancer Fight==<br />
<br />
The ''New York Times'' [http://www.nytimes.com/2005/10/27/health/27breast.html reported] on October 27, 2005 on a new National Cancer Institute study that attributed a significant decrease in the death rate from breast cancer to mammogram screening tests. The study, published in the New England Journal of Medicine, found that from 28% to 65% of the sharp 24% decrease in breast cancer death rates from 1990 to 2000 was due to screening; the remainder was attributed to new drugs used to treat the disease.<br />
<br />
Prior to this study, the value of mammogram screening had been disputed, for several reasons. In the general population, the test results in a large proportion number of false positives, about 90%. Thus, many women who are cancer-free are subjected to unnecessary procedures. Also, approximately 30% of cancers that are detected and treated would not have progressed significantly. Unfortunately, it isn't possible to distinguish between these so-called ''indolent'' cancers and those that become life-threatening, so it is routine practice to treat them all.<br />
<br />
The new study suggests that the benefits of routine mammography are more certain than earlier believed, according to Don Berry, Chairman of the biostatistics department of M. D. Anderson Cancer Center, in Houston, Texas, and the lead author of the paper. He said that the new study for the first time properly separates the effects of therapy and screening. Nonetheless, he cautioned that mammography does pose risks, and recommended that women be counselled before screening.<br />
<br />
Contributed by Bill Jefferys<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div></div>Nano12https://www.causeweb.org/wiki/chance/index.php?title=Chance_News_7&diff=1551Chance News 72005-11-05T09:34:32Z<p>Nano12: /* Fortune's Formula */</p>
<hr />
<div>Sept 26 2005 to Oct 15 2005<br />
==Quotation==<br />
<blockquote><br />
While writing my book [Stochastic Processes] I had an argument with Feller [Introuction to Probability Theory and its Applications]. He asserted that everyone said "random variable" and I asserted that everyone said "chance variable." We obviously had to use the same name in our books, so we decided the issue by a stochastic procedure. That is, we tossed for it and he won. </blockquote><br />
<br />
<p align = right> Joe Doob<br><br />
[http://www.dartmouth.edu/~chance/Doob/conversation.html Statistical Science]<br><br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Forsooth==<br />
<br />
Peter Winkler suggested our first forsooth.<br />
<br />
<blockquote>Texas beats Ohio State in their opening game <br />
of the season (Saturday Sept 10 2002). The sportscasters (legendary Brent Musburger on play-by-play or Gary Danielson on analysis) observed that of the 14 teams who have <br />
previously played in the championship game (at the end of each season) 5 <br />
have suffered an earlier defeat. "Thus," they conclude, "Ohio State can <br />
still make it to the championship game, but their chances are now less <br />
than 50%."</blockquote><br />
<br />
===Discussion===<br />
<br />
What is wrong with this?<br />
----<br />
Here are forsooths from the September 2005 issues of RSS NEWS<br />
<br />
<blockquote>'Big ticket quiz' at the start of Wimbledon:<br><br><br />
Q. How many punnets (a small light basket or other container for fruit or vegetables) of strawberries are eaten each day during the Wimbledon tournament?<br><br />
Is it (a) over 8,000, (b) over 9,000 or (c) over 10,000?</blockquote><br />
<br />
<div align="right">BBC radio 5<br><br />
20 June 2005</div><br />
<br />
<blockquote>Waiting time for foot surgery down by 500%</blockquote><br />
<br />
<div align="right">Evening News (Edinburgh)<br><br />
5 July 2005</div><br />
<br />
The next two forsooths are from the October RSS news.<br />
<br />
<blockquote>In 1996-8 when the number attending university was static, the participation of women was also static, but male participation fell.</blockquote><br />
<br />
<div align="right">The Times Higher<br><br />
21 January 2005</div><br />
<br />
<blockquote>[On the subject of congestion on the London Underground..] 'Last year 976 million of us used the tube...'</blockquote><br />
<br />
<div align="right">BBC London News<br><br />
19 May 2005</div><br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Fortune's Formula==<br />
<br />
''Fortune's Formula: Wanna Bet?''<br><br />
''New York Times Book Section'', September 25, 2005<br><br />
David Pogue<br />
<br />
This must be the kind of review that every Science writer dreams of. Pogue ends his review with:<br />
<br />
<blockquote> ''Fortune's Formula'' may be the world's first history book, gambling primer, mathematics text, economics manual, personal finance guide and joke book in a single volume. Poundstone comes across like the best college professor you ever had, someone who can turn almost any technical topic into an entertaining and zesty lecture. But every now and then, you can't help wishing there were some teaching assistants on hand to help.</blockquote><br />
<br />
The author William Poundstone is a science writer who has written a number of very successful science books. His book, ''Prisoner's dilemma: John von Neumann, game theory and the puzzle of the bomb'', was written in the style of this book. Indeed Helen Joyce, in her review of this book in Plus Magazine writes:<br />
<br />
<blockquote>This book is a curious mixture of biography, history and mathematics, all neatly packaged into an entertaining and enlightening read. </blockquote><br />
<br />
Poundstone describes himself as a visual artist who does books as a "day job.". You can learn about his art work [http://www.uiowa.edu/~iareview/tirweb/feature/poundstone/interview2.htm here].<br />
<br />
''Fortune's Formula'' is primarily the story of Edward Thorp, Claude Shannon, and John Kelly and their attempt to use mathematics to make money gambling in casinos and on the stock market. None of these did their graduate work in mathematics. Thorp and Kelly got their Phd's in physics and Shannon in Genetics. <br />
<br />
In the spring of 1955, while a graduate student at UCLA, Thorp joined a discussion on the possiblity of making money from roulette. Thorp suggested that they could taking advantage of the fact that bets are still accepted for a few second after the croupier releases the ball, and in these seconds, he could estimate what part of the wheel the ball would stop. <br />
<br />
Thorp did not pursue this and in 1959 became an instructor in mathematics at M.I.T. Here he became interested in blackjack and developed his famous card counting method for wining at blackjack. He decided to publish his method in the most prestigious journal he could find and settled on ''Proceedings of the National Academy of Sciences''. For this he needed to have a member of the Academy submit his paper. The only member in the math department was Shannon so he had to persuade him of the importance of his paper. Shannon not only agreed but in the process became fascinated by Thorp's idea for beating roulette. He agreed to help Thorp carry this out. They built a roulette machine in Shannon's basement. It worked fine there in trial runs but not so well in the casino so they did not pursue this method of getting rich. <br />
<br />
Of course Thorp is best known for showing that blackjack is a favorable game and giving a method to exploit this fact. Shannon is best known for his work in information theory. Kelly is known his method for gambling in a favorable game. This plays a central role in Poundstone's book and is probably why Pogue felt that it would help if he had a teaching assistant. Poundstone tries to explain Kelly's work in many different ways but what he really needed to understand it is an example but this required too many formulas for a popular book. So we shall include an example from Chance News 7.09. <br />
<br />
Writing for Motley Fool, 3 April 1997 Mark Brady complained about the inumeracy of the general public and gave a number of examples including this one:<br />
<br />
<blockquote> Fear of uncertainty and innumeracy are synergistic. Most people cannot do the odds. What is a better deal over a year? A 100% safe return with 5 percent interest or a 90 percent safe return with a 20 percent return. For the first deal, your return will be 5% percent. For the second, your return will be 8%. Say you invest $1000 10 times. Your interest for the 9 successful deals will be 9000 x 0.2 or 1800. Subtract the 1000 you lost on the 10th deal and you get a $800 return on your original $10,000 for 8 percent.</blockquote><br />
<br />
Peter Doyle suggested that a better investment strategy in this case is:<br />
<br />
Faced with a 100 percent-safe investment returning 5 percent and a 90 percent-safe investment returning 20%, you should invest 20% of your funds in the risky investment and 80% in the safe investment. This gives you an effective return of roughly 5.31962607969968292 percent. <br />
<br />
Peter is using a money management system due to J. L. Kelly (1956: "A new interpretation of information rate," ''Bell System Technical Journal'', '''35'''). Kelly was interested in finding a rational way to invest your money faced with one or more investment schemes, each of which has a positive expected gain. He did not think it reasonable to try simply to maximize your expected return. If you did this in the Motley Fools example as suggested by Mark Brady, you would choose the risky investment and might well lose all your money the first year. We will illustrate what Kelly did propose in terms of Motley Fools example. <br />
<br />
We start with an initial capital, which we choose for convenience to be $1, and invest a fraction r of this money in the gamble and a fraction 1-r in the sure-thing. Then for the next year we use the same fractions to invest the money that resulted from the first year's investments and continue, using the same r each year. Assume, for example, that in the first and third years we win the gamble and in the second year we lose it. Then after 3 years our investment returns an amount f(r) where: <br />
<br />
<math><br />
f(r) = (1.2r + 1.05(1-r))(1.05(1-r))(1.2r + 1.05(1-r)). <br />
</math><br />
<br />
After n years, we would have n such factors, each corresponding to a win or a loss of our risky investment. Since the order of the terms does not matter our capital will be: <br />
<br />
<math><br />
f(r,n) = (1.2r + 1.05(1-r))^W(1.05(1-r))^L<br />
</math><br />
<br />
where W is the number of times we won the risky investment and L the number of times we lost it. Now Kelly calls the quantity:<br />
<br />
<math><br />
G(r) =\lim_{n \to \infty }\frac{\log(f( r,n)} {n}<br />
</math> <br />
<br />
the exponential rate of growth of our capital. In terms of G(r) our capital should grow like <math> e^{G(r)} </math>. In our example: <br />
<br />
<math><br />
\log(\frac{f(r,n)}{n}) = \frac{W}{n}\log(1.2r + 1.05(1-r)) + \frac{L}{n}\log(1.05(1-r))<br />
</math> <br />
<br />
Since we have a 90% chance of winning our gamble, the [http://en.wikipedia.org/wiki/Strong_law_of_large_numbers#The_strong_law strong law of large numbers] tells us that as n tends to infinity this will converge to <br />
<br />
<math><br />
G(r) = 0.9\log(1.2r + 1.05(1-r))+0.1\log(1.05(1-r))<br />
</math><br />
<br />
It is a simple calculus problem to show that G(r) is maximized by r = 0.2 with: <br />
G(0.2) = 0.05183. Then e^{0.05183} = 1.0532, showing that our maximum rate of growth is 5.32% as claimed by Peter. <br />
<br />
The attractiveness of the Kelly investment scheme is that, in the long run, any other investment strategy (including those where you are allowed to change your investment proportions at different times) will do less well. "In the long run and less well" means more precisely that the ratio of your return under the Kelly scheme and your return under any other strategy will tend to infinity.<br />
<br />
Thorp had a very good experience in the stock market, which is described very well by Gaeton Lion in his excellent [http://www.amazon.com/gp/product/customer-reviews/0809046377/ref=cm_cr_dp_pt/103-8647004-5865443?%5Fencoding=UTF8&n=283155&s=books review] of ''Fortune's Formula''. He writes:<br />
<br />
<blockquote> Ed Thorp succeeded in deriving superior returns in both gambling and investing. But, it was not so much because of Kelly's formula. He developed other tools to achieve superior returns. In gambling, Ed Thorp succeeded at Black Jack by developing the card counting method. He just used intuitively Kelly's formula to increase his bets whenever the odds were in his favor. Later, he ran a hedge fund for 20 years until the late 80s and earned a rate of return of 14% handily beating the market's 8% during the period. <br><br><br />
<br />
Also, his hedge fund hardly lost any value on black Monday in October 1987, when the market crashed by 22%. The volatility of his returns was far lower than the market. He did this by exploiting market inefficiencies using warrants, options, and convertible bonds. The Kelly formula was for him a risk management discipline and not a direct source of excess return. </blockquote><br />
<br />
Shannon also made a lot of money on the stock market, but did not use Kelly's formula. In his [http://www.amazon.com/gp/product/customer-reviews/0809046377/ref=cm_cr_dp_pt/103-8647004-5865443?%5Fencoding=UTF8&n=283155&s=books review] Gaeton Lion writes<br />
<br />
<blockquote>Claude Shannon amassed large wealth by recording one of the best investment records. His performance had little to do with Kelly's formula. Between 1966 and 1986, his record beat even Warren Buffet (28% to 27% respectively). Shannon strategy was similar to Buffet. Both their stock portfolios were concentrated, and held for the long term. Shannon achieved his record by holding mainly three stocks (Teledyne, Motorola, and HP). The difference between the two was that Shannon invested in technology because he understood it well, while Buffet did not. </blockquote><br />
<br />
Finally, Thorp provided the following comments for the book cover:<br />
<br />
<blockquote>From bookies to billionaires, you'll meet a motley cast of characters in this highly original, 'outside the box' look at gambling and investing. Read it for the stories alone, and you'll be surprised at how much else you can learn without even trying. --Edward O. Thorp, author of ''Beat the Dealer'' and ''Beat the Market''.</blockquote><br />
<br />
Submitted by Laurie Snell.<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Which foods prevent cancer?==<br />
<br />
Which of these foods will stop cancer? (Not so fast)<br><br />
New York Times, 27 September 2005, Sect. F, p. 1<Br><br />
Gina Kolata<br />
<br />
Among other examples, the article includes a [http://www.nytimes.com/imagepages/2005/09/26/science/20050927_CANCER_GRAPHIC.html data graphic] on purported benefits of dietary fiber in preventing colorectal cancer. Early observational studies indicated an association, but subsequent randomized experiments found no effect. <br />
<br />
More to follow.<br />
<br />
<br />
==Slices of risk and the <em>broken heart</em> concept==<br />
[http://www.gloriamundi.org/picsresources/news20050912.pdf How a Formula Ignited Market That Burned Some Big Investors],<br />
Mark Whitehouse, The Wall Street Journal, September 12, 2005.<br><br />
<br />
This on-line article relates how a statistician, David Li,<br />
unknown outside a small coterie of finance theorists, helped change the world of investing. <br />
<br />
The article focuses on a event last May when General Motors Corp's debt<br />
was downgraded to junk status, causing turmoil in some financial markets.<br />
The article gives a nice summary of the underlying financial instruments known<br />
as credit derivatives -<br />
investment contracts structured so their value depends on the behavior of some other thing or event -<br />
with exotic names like <br />
[http://en.wikipedia.org/wiki/Collateralized_debt_obligations collateralized debt obligations] and [http://en.wikipedia.org/wiki/Credit_default_swap credit-default swaps].<br />
<br />
The critical step is to estimate the likelihood that many of the companies <br />
in a pool of companies would go bust at once. <br />
For instance, if the companies were all in closely related industries,<br />
such as auto-parts suppliers, they might fall like dominoes after a catastrophic event.<br />
Such a pool would have a 'high default correlation'.<br />
<br />
In 1997, nobody knew how to calculate default correlations with any precision. <br />
Mr. Li's solution drew inspiration from a concept in actuarial science known as the <br />
<em>broken heart</em> syndrome - people tend to die faster after the death of a beloved spouse. <br />
Some of his colleagues from academia were working on a way to predict this<br />
death correlation, something quite useful to companies that sell life insurance and joint annuities.<br />
He says:<br />
<blockquote><br />
Suddenly I thought that the problem I was trying to solve was exactly like the problem these<br />
guys were trying to solve,.<br />
Default is like the death of a company, so we should<br />
model this the same way we model human life."<br />
</blockquote><br />
<br />
This gave him the idea of using [http://en.wikipedia.org/wiki/Copula_%28statistics%29 copulas], <br />
mathematical functions the colleagues had begun applying to actuarial science. <br />
Copulas help predict the likelihood of various events<br />
occurring when those events depend to some extent on one another. <br />
Until the events last May of this year, one of the most popular copulas for bond pools <br />
was the Gaussian copula, named after <br />
[http://en.wikipedia.org/wiki/Carl_Friedrich_Gauss Carl Friedrich Gauss], a 19th-century German statistician. <br />
<br />
===Further reading===<br />
* The [http://www.gloriamundi.org/picsresources/news20050912.pdf on-line article] gives more details about what went wrong in the financial markets in May and the search for a more appropriate copula to capture better the <em>broken heart</em> syndrome between companies.<br />
* [http://en.wikipedia.org/wiki/Wikipedia Wikipedia] is a very worthwhile on-line resource for definitions of technical words, such as [http://en.wikipedia.org/wiki/Copula_%28statistics%29 copula].<br />
<br />
Submitted by John Gavin.<br />
<br />
<br />
==Learning to speak via statistics and graph theory==<br />
<br />
[http://education.guardian.co.uk/tefl/teaching/story/0,15085,1576100,00.html Computer learns grammar by crunching sentences], Max de Lotbinière September 23, 2005, [http://www.guardianweekly.co.uk/ Guardian Weekly].<br><br />
[http://www.cornellsun.com/vnews/display.v/ART/2005/09/09/432118a84f6af Profs’ New Software ‘Learns’ Languages], Ben Birnbaum, 9 Sep 2005, Cornell Daily Sun.<br />
<br />
A language-learning robot may sound like science fiction but new software, developed by Cornell University psychology professor Shimon Edelman, with colleagues Zach Solan, David Horn and Eytan Ruppin from Tel Aviv University in Israel, is well on the way to constructing a computer program that can teach itself languages and make up its own sentences, the developers' claim.<br />
<br />
Unlike previous attempts at developing computer algorithms for language learning - "Automatic Distillation of Structure," or "ADIOS" for short - discovers complex patterns in raw text by repeatedly aligning sentences and looking for overlapping parts.<br />
Once it has derived a language's rules of grammar,<br />
it can then produce sentences of its own, simply from blocks of text in that language.<br />
<br />
It has been evaluated on artificial context-free grammars with thousands of rules, <br />
on natural languages as diverse as English and Chinese, <br />
on coding regions in DNA sequences and on protein data correlating sequence with function. <br />
<br />
Edelman comments:<br />
<blockquote><br />
Adios relies on a statistical method for pattern extraction and on structured generalisations <br />
- the two processes that have been implicated in language acquisition.<br />
Our experiments show that Adios can acquire intricate structures <br />
from raw data including transcripts of parents' speech directed at two- or three-year-olds.<br />
This may eventually help researchers understand how children, <br />
who learn language in a similar item-by-item fashion, and with little supervision, <br />
eventually master the full complexity of their native tongue.<br />
</blockquote><br />
<br />
[http://plus.maths.org/latestnews/may-aug05/adios/ Plus Magazine's website]<br />
offers a more logical explanation:<br />
<blockquote><br />
The ADIOS algorithm is based on statistical and algebraic methods performed on one of the most basic and versatile objects of mathematics - the graph.<br />
Given a text, the program loads it as a graph by representing each word by a node, or vertex, and each sentence by a sequence of nodes connected by lines. A string of words in the text is now represented by a path in the graph. <br><br />
<br />
Next it performs a statistical analysis to see which paths, or strings of words, occur unusually often. <br />
It then decides that those that appear most frequently - called "significant patterns" - <br />
can safely be regarded as a single unit<br />
and replaces the set of vertices in each of these patterns by a single vertex, <br />
thus creating a new, generalised, graph.<br><br />
<br />
Finally, the program looks for paths in the graph which just differ by one vertex. <br />
These stand for parts of sentences that just differ by one word (or compound of words) like "the cat is hungry" and "the dog is hungry". <br />
Performing another statistical test on the frequency of these paths, the program identifies classes of vertices, or words, that can be regarded as interchangeable, or equivalent. <br />
The sentence involved is legitimate no matter which of the words in the class - in our example "cat" or "dog" - you put in.<br><br />
<br />
This last step is then repeated recursively.<br><br />
</blockquote><br />
<br />
[http://plus.maths.org/latestnews/may-aug05/adios/ The website] uses graphs to illustrate some examples and it finishes with some reassuring words:<br />
<blockquote><br />
All this doesn't mean, of course, that the program actually "understands" what it's saying. It simply knows how to have a good go at piecing together fragments of sentences it has identified, in the hope that they are grammatically correct. So if, like me, you're prone to swearing at your computer, you can safely continue to do so: it won't answer back for a long while yet.<br />
</blockquote><br />
<br />
===Further reading===<br />
The [http://adios.tau.ac.il/ ADIOS homepage] offers an overview and more detailed description of the program.<br />
<br />
Submitted by John Gavin.<br />
<br />
==Understanding probability==<br />
<br />
Understanding Probability:Chance rules in everyday life<br><br />
Cambridge University Press 2004<br><br />
Henk Tijms<br />
<br />
Hank Tijms is Professor in Operation Research at the Vrije University in Amsterdam. This book is based on his earlier Dutch book “Spelen met Kansen.” <br />
<br />
The aim of this book is to show how probability applies to our everyday life in a way that your Uncle George could understand even if he has forgotten much of his high school math. Tijms does not try to avoid mathematics but only to postpone the formal math until the reader has seen the many applications of probability in the real world, how much fun it is, and learned to work problems and when he can’t work one how to get the answer by simulation. He learns all this in part I of the book and then he learns the more formal math in Part II.<br />
<br />
In Chapter 1 Tijms asks the reader to think about problems with surprising answers in the spirit of Susan Holmes “[http://www-stat.stanford.edu/~susan/surprise/ Probability by Surprise]” including the birthday problem and the Monty Hall problem. Readers are on their own to try to solve one or more of the problems but promised that they will see the solutions later in the book. <br />
<br />
Chapter 2 deals with the law of large numbers and introduces the concept of simulation. This theorem is explained and illustrated by problems related, for example, to coin tossing, random walks and casino games. Expected value is introduced in an informal way to be defined more carefully later in the book. For the reader who is not frightened by mathematical formulas, Tijms includes a discussion of the Kelly betting system with a footnote saying that this paragraph can be skipped at first reading. This is a fascinating topic that is widely applied in gambling and stock investment but rarely appears in a probability book.<br />
<br />
In Chapter 3 the author returns to previous problems such as the birthday problem and gambling systems and solves them first by simulation and then by mathematics. <br />
<br />
In this chapter Tijms describes Efron’s bootstrap method and uses it to solve a number of problems including a hypothetical clinical trial and to test if the famous 1970 draft lottery during the Vietnam War was fair. Again the bootstrap method has wide application but rarely occurs in an elementary probability or statistics book.<br />
<br />
Chapter 4 describes the binomial, Poisson, and hypergeomtric distributions and how to use them in solving problems such as the famous hat check problem, and a variety of interesting lottery questions. The Poisson process is discussed but again with the footnote that novice readers might want to read this at a later time.<br />
<br />
Chapter 5 is mainly about Center Limit Theorem and its many applications especially to statistics. <br />
<br />
Chapter 6 introduces Chance trees and Bayes’s rule. The tree method is used to explain a variety of problems including the Monty Hall Problem and the false-positive paradox. <br />
<br />
This is a brief description of the first six chapters which constitute Part I of the book. Now the fun is over. Part 2 called “Essentials of probability” looks like the traditional first chapters in a standard probability book. But the reader has already found how exciting probability is, has a good intuitive idea of the basic concepts and has worked many of the interesting problems at the end of each chapter either using math or simulation. For some students this might allow them to actually enjoy Part 2. But your Uncle George may want to quit while they are ahead. <br />
<br />
Tijms writes with great clarity and his enthusiasm for probability in the real world is contagious. We were delighted to see, as acknowledged in the preface, that Tijms included several of the more interesting problems discussed in Chance News, often going well beyond what we had said in our discussion of the problem. <br />
<br />
This book presents a completely new way to go about teaching a first course in probability and we think those who teach such a course should consider trying it out.<br />
<br />
===Discussion===<br />
<br />
(1) In the days of Basic we required all students to learn Basic in their first math course so we could assume that students could write programs to simulate probability problems and so me made heavy use of simulation as suggested in this book. The author uses Pascal in his book. What present language do you think is easiest for a student with no computing experience to learn?<br />
<br />
We asked Professor Tijms what the situation was in math departments in Europe and he replied:<br />
<br />
<blockquote>In math departments of universities and polytechnic schools in Europe students learn to write computer programs. In my university they still learn to program in Java and C++ ( in previous days Pascal), but I see in the Netherlands the trend that the instructors think it is sufficient if the students are able to program in Matlab. <br><br><br />
<br />
In ny book I have chosen to formulate the simulation programs in Pascal because of the clarity and the simplicity of the language, though this language is hardly used anymore. The introductory probability course at my university is given before they have learned to program, but this does not prevent them of simulating probability problems by using Excel. In the simulation of many elementary probability problems a random-number generator alone suffices to simulate those problems and so Excel can be used. In the second year they have mastered Matlab, a perfect tool with its excellent graphics to simulate many challenging probability problems ( they really like it, in particular when it concerns problems such as the problems 2.24-2.45 in chapter 2 and the problems 5.11-5.13 in chapter 5). <br />
</blockquote><br />
<br />
<br />
(2) Do you think that probability books should include data to test probability models that are said to describe real world problems? If so name some models that you think would pass such a test and some that you think might not.<br />
<br />
Submitted by Laurie Snell<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Societies worse off when they have God on their side==<br />
<br />
[http://www.timesonline.co.uk/article/0,,2-1798944,00.html Societies worse off when they have God on their side]<br><br />
Timesonline, September 27, 2005<br><br />
Ruth Gledhill<br />
<br />
[http://moses.creighton.edu/JRS/2005/2005-11.html Cross-national correlations of quantifiable societal health with popular religiosity and secularism in the prosperous democracies]<br><br />
Journal of Religion & Society, Vol.7(2005)<br><br />
Gregory S. Paul<br />
<br />
In the Times article we read:<br />
<br />
<blockquote>According to the study, belief in and worship of God are not only unnecessary for a healthy society but may actually contribute to social problems.<br><br><br />
Many liberal Christians and believers of other faiths hold that religious belief is socially beneficial, believing that it helps to lower rates of violent crime, murder, suicide, sexual promiscuity and abortion. The benefits of religious belief to a society have been described as its “spiritual capital”. But the study claims that the devotion of many in the US may actually contribute to its ills. <br />
</blockquote><br />
<br />
Gregory Paul is a dinosaur paleontologist and on an [http://www.abc.net.au/worldtoday/indexes/2005/twt_20050928.htm interview] on Australian ABC radio Paul said that, being a paleontologist, for many years he had to deal with the issue of creationism versus evolutionary science in the U.S and his interest in evolutionary science prompted him to look at whether there was any link between the religiosity of a society and how well that society functions. <br />
<br />
If you look at Paul's article you will find very little technical statistical analysis, for example, he did not carry out a regression analysis. Rather he rests his case on the series of scatterplots.<br />
<br />
Paul describes his data sources as:<br />
<br />
<blockquote>Data sources for rates of religious belief and practice as well as acceptance of evolution are the 1993 Environment I (Bishop) and 1998 Religion II polls conducted by the International Social Survey Program (ISSP), a cross-national collaboration on social science surveys using standard methodologies that currently involves 38 nations. The last survey interviewed approximately 23,000 people in almost all (17) of the developed democracies; Portugal is also plotted as an example of a second world European democracy. Results for western and eastern Germany are combined following the regions' populations. England is generally Great Britain excluding Northern Ireland; Holland is all of the Netherlands. The results largely agree with national surveys on the same subjects; for example, both ISSP and Gallup indicate that absolute plus less certain believers in a higher power are about 90% of the U.S. population. The plots include Bible literalism and frequency of prayer and service attendance, as well as absolute belief in a creator, in order to examine religiosity in terms of ardency, conservatism, and activities. </blockquote><br />
<br />
Here are the countries Paul considered with the abbreviations used on the graphics. <br />
<br />
A = Australia, C = Canada, D = Denmark, E = Great Britain, F = France, G = Germany,<br />
H = Holland, I = Ireland, J = Japan, L = Switzerland, N = Norway, P = Portugal, R = Austria,<br />
S = Spain, T = Italy, U = United States, W = Sweden, Z = New Zealand.<br />
<br />
There seems to be no agreement as to which countries are developed democracies. For example Paul might have included Greece and Belgium, Finland, and others but the data may have determined his choice. Paul comments that he added Portugal as an example of a second world democracy. <br />
<br />
Paul's anaysis of the data includes a series of 9 Figures which are available at the end of the article and are the most interesting part of the study. If you try printing Paul's article you will only get the first of his 9 Figures. When you look at the [http://moses.creighton.edu/JRS/2005/2005-11.html web version] you will still see only Figure 1 but the others can be viewed by selecting the numbers from 2 to 9 on the left side of Figure 1.<br />
<br />
Figure 1 deals with the proportion of people who accept human evolution which is interesting but not as relevant to the welfare of the people as others so we will look at Figure 2.<br />
<br />
[[Image:religion2.png|500px|center|Source:Gregory Paul]]<br />
<br />
Each Figure iprovides 5 separate scatterplots. Ïn Figure 2 we see that the U.S. has largest number--between 6 and 7-- of homicides per 100,000 and Spain has the lowest number with less than 1 homicide per 100,000. We also see that the U.S. has the highest proportion of people, about 25%, who take the bible literally while several countries have less than 10% such people.<br />
<br />
What we cannot do is compare the number of homicides per thousand between those who take the bible literally and those who are agnostics or atheists which is what we would really want to know. Presumably the data did not permit this comparison. <br />
<br />
[[Image:religion3.png|500px|center|Source:Gregory Paul]]<br />
<br />
Figure 3 deals with "14-24 year old suicides per 100,000". Here the U.S. is in about the middle.<br />
<br />
Figure 4 deals with the "under-five mortalities per 1000 births".<br />
<br />
[[Image:religion4.png|500px|center|Source:Gregory Paul]]<br />
<br />
Ignoring Portugal, the U.S. has the highest number of under-five mortalities per 1000 births-- between 7 and--8 while several countries have only 4.<br />
<br />
The other figures can be seen at end of Paul's article. They deal with life expectancy, sexually transmitted diseases, abortion and 15-16 year old pregnancies. Life expectancy is the smallest in the U.S. and for sexually transmitted diseases, abortion and 15-17 year old prenacies the U.S. is at the top of the graphs and in fact these look like outliers.<br />
<br />
Well, this study does not by itself justify the Times hedline: "Societies worse off when they have God on their side." Paul himself would not claim this. He writes:<br />
<br />
<blockquote> This study is a first, brief look at an important subject that has been almost entirely neglected by social scientists. The primary intent is to present basic correlations of the elemental data. Some conclusions that can be gleaned from the plots are outlined. This is not an attempt to present a definitive study that establishes cause versus effect between religiosity, secularism and societal health. It is hoped that these original correlations and results will spark future research and debate on the issue.</block<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div></div>Nano12https://www.causeweb.org/wiki/chance/index.php?title=Chance_News_9&diff=1550Chance News 92005-11-05T09:34:28Z<p>Nano12: /* Forsooth */</p>
<hr />
<div>==Quotation==<br />
Å quotation will be added here.<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Forsooth==<br />
Forsooth items should be added here.<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Supreme Court Nominee Alito: Statistics Misleading?==<br />
An [http://www.salon.com/politics/war_room/2005/10/31/jury/index.html article] in Salon.com for October 31 discusses the first-degree murder trial, Riley v. Taylor. The defendant Riley was African-American; at the trial, the prosecution used its peremptory challenges to eliminate all three of the African-Americans on the jury panel. In the same county that year, there were three other first-degree murder trials, and in every one of those cases all of the African-American jurors were struck.<br />
<br />
A majority of the judges on the appeals court thought that there was evidence that jurors were struck for racial reasons. According to them, a simple calculation indicates that there should have been five African-American jurors amongst the forty-eight that were empanelled. However, there were none. To these judges, this was clear evidence of racial motivaion in the striking of such jurors.<br />
<br />
Judge Alito dissented. He called the majority's analysis simplistic, and stated that although only 10% of the U.S. population is left-handed, five of the last six people elected president of the United States were left-handed. He asked rhetorically whether this indicated bias against right-handers amongst the U.S. electorate.<br />
<br />
The majority responded that there is no provision in the Constitution that protects persons from discrimination based on whether they are right-handed or left-handed, and that to compare these cases with the handedness of presidents ignores the history of racial discrimination in the United States.<br />
<br />
===Questions===<br />
<br />
1) Assuming that Judge Alito is correct about the proportion of left-handers in the U.S. population, what is the probability that five of the last six presidents elected would be left-handed?<br />
<br />
2) Is Judge Alito's comparison biased by the fact that he chose just the last six presidents? Presumably he believed that the president just before this group was right-handed, otherwise he would have included him in the sample and said "six of the last seven presidents." What is the relevant statistic?<br />
<br />
3) When the decision came down in 2001, the last six people elected president were George W. Bush, Clinton, George H. W. Bush, Reagan, Carter and Nixon. Of these, Clinton and George H. W. Bush were left-handed. Ford, who was left-handed, was not elected president (or even vice-president); he became president upon the resignation of Richard Nixon. Reagan may have been left-handed as a child, but he wrote right-handed so his case isn't clear; the Reagan Presidential Library [http://www.reagan.utexas.edu/archives/reference/facts.html says] that he was "generally right-handed." Judge Alito may have been confused, including on his list Ford (who was not elected) and George W. Bush (who is not left-handed, although his father is), as well as Reagan. The other left-handed presidents were Truman and Garfield. Hoover is found on some lists of left-handed presidents, but according to the Hoover Institution, he was not left-handed. How does this information affect Alito's argument?<br />
<br />
4) Suppose that 5/48 of the jury pool were African-American. What is the probability that no juror amongst the 48 selected would have been African-American? How does this compare with the actual statistics of left-handed presidents? Does the same objection apply to this case as might apply to Alito's example?<br />
<br />
5) What is your opinion? Is there clear statistical evidence of racial bias in the use of peremptory challenges in this county?<br />
<br />
6) What does it say about our judiciary that Judge Alito could get his facts as wrong as he did, and that none of the judges in the majority caught the errors?<br />
<br />
Contributed by Bill Jefferys<br />
<br />
==item2==<br />
Replace item2 by the name of your article.</div>Nano12https://www.causeweb.org/wiki/chance/index.php?title=Chance_News_8&diff=1549Chance News 82005-11-05T09:34:25Z<p>Nano12: /* The Poisson distribution and the Supreme Court */</p>
<hr />
<div>Oct 15 to Oct 30<br />
<br />
==Quotation==<br />
<blockquote>One more fagot of these adamantine bandages, is, the new science of Statistics. It is a rule, that the most casual and extraordinary events -- if the basis of population is broad enough -- become matter of fixed calculation. It would not be safe to say when a captain like Bonaparte, a singer like Jenny Lind, or a navigator like Bowditch, would be born in Boston: but, on a population of twenty or two hundred millions, something like accuracy may be had. Ralph Waldo Emerson Fate</blockquote><br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Forsooth==<br />
Here's another Forsooth from the October issue of RSS News.<br />
<blockquote>Your'e more likely to die in a fire in Strathclyde than anywhere else in the country</blockquote><br />
<br />
<div align="right">BBC1 mews bullietin<br><br />
11 May 2005</div><br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==The Poisson distribution and the Supreme Court==<br />
The Poisson distribution and the Supreme Court<br><br />
''Journal of the American Statistical Association'' 31, no. 195 ,(1936), 376-80<br><br />
W. Allen Wallis<br />
<br />
Supreme Court Appointments as a Poisson distribution<br><br />
''American Journal of Political Science'', 26, No.1, February 1982<br><br />
S. Sidney Ulmer<br />
<br />
This is not current news, but since Supreme Court appointments are in the news we felt that these articles might make an interesting class discussion.<br />
<br />
In 1936 statistician Allen Wallis suggested that a Poisson distribution can approximate the number of U.S. Supreme Court appointments in a given year. In his Table 1 Wallis provided the number appointed in each year over the intervals with different numbers of Justices on the Supreme Court: 1790-1806 (6) 1807-1836 (7), and 1837-1932 (9). Actually there were 10 in the years 1963 to 1967 which Wallis called "negligible exceptions."<br />
<br />
[[Image:wallis1.png|500px|center]]<br />
<br />
Wallis then restricts himself to the years 1837-1932 and finds that a Poisson distribution with mean .5 can approximate the number of court appointments in a year. His results are shown in his Figure II:<br />
<br />
[[Image:wallis2.png|500px|center]]<br />
<br />
In his article, Sidney Ulmer updated the data to 1980 and also includes data from the early Supreme Courts with 6 and 7 members. Thus his data covers the years 1790--1980. His Table 1 compares the actual number of appointments in a year with the expected number of appointments assuming a Poisson distribution with mean 5.13.<br />
<br />
[[Image:ulmer1.png|500px|center]]<br />
<br />
In his Table II Ulmer limits the data to the 9 member Supreme Courts: 1837 to 1862 and 1869-1980).<br />
<br />
[[Image:ulmer2.png|500px|center]]<br />
<br />
Testing the goodness of fits, Ulmer argues that the fit with the varying size Supreme Courts is just as good as with fixed size Supreme Courts.<br />
<br />
===DISCUSSION===<br />
<br />
(1) What is the probability that a President will make 2 or more appointments to the Supreme Court during a 4-year term? What is the probability a President makes no appointments during a 4-year term? Has this ever happened?<br />
<br />
(2) Do you agree with Ulmer that there is no reason to limit the data to years with the Supreme Court is the same size?<br />
<br />
(3) Obtain the data needed to update Ulmer's results to today and provide Tables that correspond to Ulmer's Tables 1 and 2. Add your Tables to this Chance News and make your data available to make it easier to update this in future years.<br />
<br />
Contributed by Laurie Snell<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Possible Cancer Cluster in Connecticut==<br />
Pratt Agrees to Increase Funding for Brain Cancer Study <br><br />
''The Associated Press''<br><br />
October 11, 2005<br><br />
Stephen Singer<br><br />
<br />
<br />
In a case that seems eerily familiar to the leukemia cancer cluster made famous by the book and movie, ''A Civil Action'', researchers are trying to determine whether or not a cancer cluster exists among workers at Pratt & Whitney, a company that manufactures jet engines. Over one hundred former or current Pratt & Whitney employees have been identified as having a relatively rare type of fatal brain tumor known as glioblastoma multiforme, which strikes 3 people per 100,000 every year. Many of these workers have been exposed to metals and chemical substances, including TCE (trichloroethylene), which is an engine degreaser. TCE is the same carcinogenic chemical that was dumped in the 1960’s and 1970’s by the chemical company, WR Grace, in Woburn, MA, and that was found to have contaminated the drinking water in two of the town’s wells. <br><br />
<br />
<br />
Prior to the recent announcement that the funding is being increased from $6 million dollars to $12 million dollars, this medical study was already being described as the largest occupational health study ever conducted. It covers 250,000 people who worked at any of the seven Connecticut Pratt & Whitney plants from 1952 to 2001. So far, at least 125 cases of brain cancer have been documented, according to the lawyer who represents dozens of individuals and family members.<br><br />
<br />
<br />
The study falls under the auspices of the Connecticut Department of Public Health. However, due to the overwhelming cost and scope of the study, Pratt & Whitney is funding the project. Since Pratt is paying for the study, they chose the researchers, a team from the University of Pittsburgh. The project began three years ago, and the results are expected to be available between 2007 and 2009.<br><br />
<br />
<br />
In the meantime, this case faces many of the obstacles common in the quest to establish whether or not a cancer cluster exists, such as proving causation, the fact that it can take a long time (sometimes 5-40 years) after exposure for true problems to show up, and finding the people who were exposed & convincing them to participate in the study. Additionally, there are legal difficulties for the families involved, including Connecticut’s statute of limitations laws, the length of time it takes investigators to reach a conclusion, the cost of litigation, and the “deep pockets” of a company like Pratt & Whitney.<br><br />
<br />
<br />
This case study provides a current example of an ongoing investigation into a possible cancer cluster. Will it ultimately be found to be a coincidence cluster or proven to be a true cancer cluster? Does it make sense that the researchers are including in the study everyone who worked at Pratt over a fifty year period, even those who only worked there for a brief time period and those who were not directly exposed to toxic substances (i.e. office workers)? Could the researchers possibly have an unconscious bias in favor of the company that is funding their research? If the company doesn’t fund the research, then who should? Is there some other way to structure such investigations, so that the company involved pays for the study, but is not allowed to choose the researchers and directly fund them?<br><br />
<br />
<br />
'''Further Reading'''<br><br />
<br />
• “Rare Cancer Found in Workers”, ''The New York Times'', March 10, 2002, Jane Gordon<br><br />
• “Scientist: Pratt Commits to Cancer Study”, ''The Hartford Courant'', May 19, 2005<br><br />
• “Participation in Cancer Study at Pratt Lagging”, ''The Hartford Courant'', October 12, 2005, Paul Marks<br><br />
• ''The New Haven Advocate'' has had more than a dozen articles that explain the working conditions at Pratt & Whitney, and also chronicle the history & progression of this case. These articles have been investigated and written primarily by Carole Bass, Associate Editor. A few of the articles are listed below. <br> <br />
-“Worked to Death”, August 2, 2001, Carole Bass & Camille Jackson<br><br />
-“Talking Cure”, October 28, 2004, Dave Goldberg<br><br />
-“Time’s Not on Their Side”, January 20, 2005, Carole Bass<br><br />
-“The Brains Behind the Brain”, October 20, 2005, Carole Bass <br><br />
For the early New Haven Advocate articles (i.e., 2001-2002) on this subject, go to http://old.newhavenadvocate.com/workedtodeath/index.html<br> <br />
For the articles since 2002, go to <br><br />
http://www.newhavenadvocate.com and search for Pratt & Whitney.<br><br />
<br />
Submitted by Josephine Rodriguez.<br />
<br />
==A record powerball lottery jackpot==<br />
<br />
On Saturday Oct 22, 2005 the powerball lottery had a record powerball jackpot of 340 million dollars. <br />
<br />
When you buy a ticket for this lottery, you specify five distinct numbers from 1 to 55, which we call basic numbers and one number from 1 to 42 called the bonus number. To win the Jackpot your 5 basic numbers and your bonus number must agree with a random choice of 5 basic numbers and one bonus number chosen by the lottery officials. The number of possible tickets is:<br />
<br />
<center><math>{55 \choose 5} 42 = </math> 146,107,962</center><br />
<br />
Thus if you buy a single ticket, the probability of having a winning jackpot ticket is<br />
<br />
<center> <math>{1} \over {146107962}</math> = .000000006844...</center><br />
<br />
The powerball website and the media expresses this by saying that the odds that you have a winning jackpot ticket is 1 in 146,107,962. <br />
<br />
Whenever there is a record jackpot, the news writers look for suggestions for other rare events that might be more familiar to its readers. <br />
<br />
Our own favorite was suggested by Fred Hoppe: if you toss a coin 27 times your chance of getting 27 heads in a row is greater than your chance of having a winning jackpot ticket when you buy a single ticket. (<math> 2^{27} = 134217728</math> and so there are 134,217,728 possible sequences of heads and tails and only 1 has all heads.)<br />
<br />
In an article for the ''Omaha World-Herald'' Oct 18, 2005 , Robynn Tysver writes:<br />
<br />
<blockquote> You have a greater chance of getting killed by lightning than winning this week's 340 million Powerball jackpot. You also have a greater chance of drowning in a bathtub. The lifetime odds of getting killed by lightning are one in 56,439, and the lifetime odds of dying while in or falling into a bathtub are one in 10,582, according to the National Safety Council. <br />
</blockquote><br />
<br />
These are not even in the ballpark. The ''Minneapolis Star Tribune'' consulted mathematicians David Bressoud and Douglas Arnold who contributed the following:<br />
<br />
According to Arnold you have a seven times better chance of becoming a saint. And Bressoud notes that you're six times more likely to get elected president of the United States. But they also provide the following more interesting estimates:<br />
<br />
<blockquote>Bressoud: "If you buy 10 tickets a week, every week, it would take you 280,000 years before you could expect to win."<br><br><br />
<br />
Arnold: "If you were to select a group of Powerball numbers every minute for 138 years, you would have about a 50 percent chance of picking the winning Powerball ticket." <br><br><br />
<br />
It is not clear what Bressoud means by "expect to win". We can check this by a simple calculation (simple for Mathematica). Let q(n) be the probability that you if you buy n tickets you fail to get a winning jackpot ticket . Then:<br />
<br />
<center> <math> \left(\frac{146107961}{146107962}\right) ^n = q(n) </math></center><br />
<br />
The average number of weeks in a year is 52.177457 so If you buy 10 tickets a week, every week for 280,000 years you will buy about 146,097,000 tickets. Using this number for n in our formula we find that you have about a 37% chance of not getting a winning lottery ticket or a 63% chance of getting one. We would not "expect to win" with a 63% chance of winning but others may. Using our formula for q(n) we find that if we buy 10 tickets a week, every week for 830,000 years you will have about a 95% chance of getting at least one winning lottery ticket which seems to us more appropriate for expecting to win. <br />
<br />
Consider now Arnold's example. Our colleague Dana Williams found that you need to buy a ticket for about 101 million lottery offerings to have about a 50% chance of getting at least one winning lottery ticket. There are an average of 525,946.766 minutes in a year. Dividing 101 million by this number gives 192.035. Thus Arnold's 138 years should be 192 years.<br />
<br />
We asked Professor Arnold about this and he replied:<br />
<br />
<blockquote> That number, which was quoted in the ''Star Tribune'' was an off-the-top-of-my-head calculation made when the reporter called me on<br />
the phone with no warning. Right ballpark, but not very accurate. Later I redid the calculation carefully.</blockquote><br />
<br />
Arnold's computations were similar to ours but he used a greater accuracy for the number of independent lotteries you have to buy to have a 50% chance of choosing the jackpot numbers at least once. His answer to this was 101,274,322. Using this, Arnold's estimate for the number of years, buying a ticket every minute, to have a 50% chance of winning a jackpot is193 years instead of our estimate of 192 years.<br />
<br />
Arnold said that he also estimated the expected value of a $1 ticket. To do this he needed an estimate for the number of tickets sold. He was told that a reasonable estimate was 106 million. In calculating the expected value of a $1 ticket he used the cash value of 164.4 million dollars instead of the annuity payout of 340 million dollars. He also took into account the possibility of having to share the jackpot. Doing this he got an expected value of exactly $1, just the price of the ticket. He commented that if he took into account the taxes the expected value would be more like 80 cents making even this lottery an unfavorable event.<br />
<br />
The news writers also gave a lot of coverage of Senator Gregg (Chairman of the Senate Budget Committee) winning $853,492 for getting the second highest prize: getting the 5 basic numbers correct but note the bonus number. Normally the prize for getting this is $200,000 cash but Gregg was the beneficiary of recent change in the powerball lottery. <br />
<br />
The powerball officials have found that increasing the size of the jackpot can increase the ticket sales because of the public's interest in large jackpots. They do this by increasing the number of possible basic numbers. When they started in 1992, to get the jackpot you had to get the 5 basic numbers chosen from 45 numbers and the 1 bonus number chosen from 45 number correct. Here are the changes so far<br />
<br />
<center><br />
1992 5 of 45 1 of 45<br><br />
1997 5 or 49 1 of 42<br><br />
2002 5 of 55 1 of 42<br><br />
2005 5 of 55 1 of 42<br><br />
</center><br />
<br />
While the lottery officials want to have higher jackpots, they also do not want too long a period between jackpots. Normally the increase in the size of the lottery, when no one wins the jackpot, is determined by the amount taken in in this unsuccessful drawing. This was recently changed so that, when a new record jackpot occurs and no-one wins it, at most 25 million dollars are added to the Jackot until someone wins the jackpot. The money save by this is added to the second prize.<br />
<br />
When the 340 million jackpot was won, 49 players had the five basic numbers correct but not the bonus numbers. For these winners the $200,000 prize had 653,492 added to their prize so they each won $853,492. If they chosen the Powerball play option for an extra $1 their $200,000 would have been multiplied by 2,3,4, or 5 with equal probabilities. Thus if Gregg had chosen the Powerball play option, and been lucky, he would have won 1,653,492 dollars that he could add to his 15 or so million dollars he has in stocks. <br />
<br />
===DISCUSSION===<br />
<br />
(1) Do you think it is fair to advertise the lottery prize as 340 million when the cash prize is only 164.4 million?<br />
<br />
(2) What is the probability of winning the second prize?<br />
<br />
(3) Assuming that the estimate 106 million for the number of tickets sold find the expected number of second prize winners.<br />
<br />
==Mammograms Validated as Key in Cancer Fight==<br />
<br />
The ''New York Times'' [http://www.nytimes.com/2005/10/27/health/27breast.html reported] on October 27, 2005 on a new National Cancer Institute study that attributed a significant decrease in the death rate from breast cancer to mammogram screening tests. The study, published in the New England Journal of Medicine, found that from 28% to 65% of the sharp 24% decrease in breast cancer death rates from 1990 to 2000 was due to screening; the remainder was attributed to new drugs used to treat the disease.<br />
<br />
Prior to this study, the value of mammogram screening had been disputed, for several reasons. In the general population, the test results in a large proportion number of false positives, about 90%. Thus, many women who are cancer-free are subjected to unnecessary procedures. Also, approximately 30% of cancers that are detected and treated would not have progressed significantly. Unfortunately, it isn't possible to distinguish between these so-called ''indolent'' cancers and those that become life-threatening, so it is routine practice to treat them all.<br />
<br />
The new study suggests that the benefits of routine mammography are more certain than earlier believed, according to Don Berry, Chairman of the biostatistics department of M. D. Anderson Cancer Center, in Houston, Texas, and the lead author of the paper. He said that the new study for the first time properly separates the effects of therapy and screening. Nonetheless, he cautioned that mammography does pose risks, and recommended that women be counselled before screening.<br />
<br />
Contributed by Bill Jefferys<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div></div>Nano12https://www.causeweb.org/wiki/chance/index.php?title=Chance_News_7&diff=1548Chance News 72005-11-05T09:34:19Z<p>Nano12: /* Discussion */</p>
<hr />
<div>Sept 26 2005 to Oct 15 2005<br />
==Quotation==<br />
<blockquote><br />
While writing my book [Stochastic Processes] I had an argument with Feller [Introuction to Probability Theory and its Applications]. He asserted that everyone said "random variable" and I asserted that everyone said "chance variable." We obviously had to use the same name in our books, so we decided the issue by a stochastic procedure. That is, we tossed for it and he won. </blockquote><br />
<br />
<p align = right> Joe Doob<br><br />
[http://www.dartmouth.edu/~chance/Doob/conversation.html Statistical Science]<br><br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Forsooth==<br />
<br />
Peter Winkler suggested our first forsooth.<br />
<br />
<blockquote>Texas beats Ohio State in their opening game <br />
of the season (Saturday Sept 10 2002). The sportscasters (legendary Brent Musburger on play-by-play or Gary Danielson on analysis) observed that of the 14 teams who have <br />
previously played in the championship game (at the end of each season) 5 <br />
have suffered an earlier defeat. "Thus," they conclude, "Ohio State can <br />
still make it to the championship game, but their chances are now less <br />
than 50%."</blockquote><br />
<br />
===Discussion===<br />
<br />
What is wrong with this?<br />
----<br />
Here are forsooths from the September 2005 issues of RSS NEWS<br />
<br />
<blockquote>'Big ticket quiz' at the start of Wimbledon:<br><br><br />
Q. How many punnets (a small light basket or other container for fruit or vegetables) of strawberries are eaten each day during the Wimbledon tournament?<br><br />
Is it (a) over 8,000, (b) over 9,000 or (c) over 10,000?</blockquote><br />
<br />
<div align="right">BBC radio 5<br><br />
20 June 2005</div><br />
<br />
<blockquote>Waiting time for foot surgery down by 500%</blockquote><br />
<br />
<div align="right">Evening News (Edinburgh)<br><br />
5 July 2005</div><br />
<br />
The next two forsooths are from the October RSS news.<br />
<br />
<blockquote>In 1996-8 when the number attending university was static, the participation of women was also static, but male participation fell.</blockquote><br />
<br />
<div align="right">The Times Higher<br><br />
21 January 2005</div><br />
<br />
<blockquote>[On the subject of congestion on the London Underground..] 'Last year 976 million of us used the tube...'</blockquote><br />
<br />
<div align="right">BBC London News<br><br />
19 May 2005</div><br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Fortune's Formula==<br />
<br />
''Fortune's Formula: Wanna Bet?''<br><br />
''New York Times Book Section'', September 25, 2005<br><br />
David Pogue<br />
<br />
This must be the kind of review that every Science writer dreams of. Pogue ends his review with:<br />
<br />
<blockquote> ''Fortune's Formula'' may be the world's first history book, gambling primer, mathematics text, economics manual, personal finance guide and joke book in a single volume. Poundstone comes across like the best college professor you ever had, someone who can turn almost any technical topic into an entertaining and zesty lecture. But every now and then, you can't help wishing there were some teaching assistants on hand to help.</blockquote><br />
<br />
The author William Poundstone is a science writer who has written a number of very successful science books. His book, ''Prisoner's dilemma: John von Neumann, game theory and the puzzle of the bomb'', was written in the style of this book. Indeed Helen Joyce, in her review of this book in Plus Magazine writes:<br />
<br />
<blockquote>This book is a curious mixture of biography, history and mathematics, all neatly packaged into an entertaining and enlightening read. </blockquote><br />
<br />
Poundstone describes himself as a visual artist who does books as a "day job.". You can learn about his art work [http://www.uiowa.edu/~iareview/tirweb/feature/poundstone/interview2.htm here].<br />
<br />
''Fortune's Formula'' is primarily the story of Edward Thorp, Claude Shannon, and John Kelly and their attempt to use mathematics to make money gambling in casinos and on the stock market. None of these did their graduate work in mathematics. Thorp and Kelly got their Phd's in physics and Shannon in Genetics. <br />
<br />
In the spring of 1955, while a graduate student at UCLA, Thorp joined a discussion on the possiblity of making money from roulette. Thorp suggested that they could taking advantage of the fact that bets are still accepted for a few second after the croupier releases the ball, and in these seconds, he could estimate what part of the wheel the ball would stop. <br />
<br />
Thorp did not pursue this and in 1959 became an instructor in mathematics at M.I.T. Here he became interested in blackjack and developed his famous card counting method for wining at blackjack. He decided to publish his method in the most prestigious journal he could find and settled on ''Proceedings of the National Academy of Sciences''. For this he needed to have a member of the Academy submit his paper. The only member in the math department was Shannon so he had to persuade him of the importance of his paper. Shannon not only agreed but in the process became fascinated by Thorp's idea for beating roulette. He agreed to help Thorp carry this out. They built a roulette machine in Shannon's basement. It worked fine there in trial runs but not so well in the casino so they did not pursue this method of getting rich. <br />
<br />
Of course Thorp is best known for showing that blackjack is a favorable game and giving a method to exploit this fact. Shannon is best known for his work in information theory. Kelly is known his method for gambling in a favorable game. This plays a central role in Poundstone's book and is probably why Pogue felt that it would help if he had a teaching assistant. Poundstone tries to explain Kelly's work in many different ways but what he really needed to understand it is an example but this required too many formulas for a popular book. So we shall include an example from Chance News 7.09. <br />
<br />
Writing for Motley Fool, 3 April 1997 Mark Brady complained about the inumeracy of the general public and gave a number of examples including this one:<br />
<br />
<blockquote> Fear of uncertainty and innumeracy are synergistic. Most people cannot do the odds. What is a better deal over a year? A 100% safe return with 5 percent interest or a 90 percent safe return with a 20 percent return. For the first deal, your return will be 5% percent. For the second, your return will be 8%. Say you invest $1000 10 times. Your interest for the 9 successful deals will be 9000 x 0.2 or 1800. Subtract the 1000 you lost on the 10th deal and you get a $800 return on your original $10,000 for 8 percent.</blockquote><br />
<br />
Peter Doyle suggested that a better investment strategy in this case is:<br />
<br />
Faced with a 100 percent-safe investment returning 5 percent and a 90 percent-safe investment returning 20%, you should invest 20% of your funds in the risky investment and 80% in the safe investment. This gives you an effective return of roughly 5.31962607969968292 percent. <br />
<br />
Peter is using a money management system due to J. L. Kelly (1956: "A new interpretation of information rate," ''Bell System Technical Journal'', '''35'''). Kelly was interested in finding a rational way to invest your money faced with one or more investment schemes, each of which has a positive expected gain. He did not think it reasonable to try simply to maximize your expected return. If you did this in the Motley Fools example as suggested by Mark Brady, you would choose the risky investment and might well lose all your money the first year. We will illustrate what Kelly did propose in terms of Motley Fools example. <br />
<br />
We start with an initial capital, which we choose for convenience to be $1, and invest a fraction r of this money in the gamble and a fraction 1-r in the sure-thing. Then for the next year we use the same fractions to invest the money that resulted from the first year's investments and continue, using the same r each year. Assume, for example, that in the first and third years we win the gamble and in the second year we lose it. Then after 3 years our investment returns an amount f(r) where: <br />
<br />
<math><br />
f(r) = (1.2r + 1.05(1-r))(1.05(1-r))(1.2r + 1.05(1-r)). <br />
</math><br />
<br />
After n years, we would have n such factors, each corresponding to a win or a loss of our risky investment. Since the order of the terms does not matter our capital will be: <br />
<br />
<math><br />
f(r,n) = (1.2r + 1.05(1-r))^W(1.05(1-r))^L<br />
</math><br />
<br />
where W is the number of times we won the risky investment and L the number of times we lost it. Now Kelly calls the quantity:<br />
<br />
<math><br />
G(r) =\lim_{n \to \infty }\frac{\log(f( r,n)} {n}<br />
</math> <br />
<br />
the exponential rate of growth of our capital. In terms of G(r) our capital should grow like <math> e^{G(r)} </math>. In our example: <br />
<br />
<math><br />
\log(\frac{f(r,n)}{n}) = \frac{W}{n}\log(1.2r + 1.05(1-r)) + \frac{L}{n}\log(1.05(1-r))<br />
</math> <br />
<br />
Since we have a 90% chance of winning our gamble, the [http://en.wikipedia.org/wiki/Strong_law_of_large_numbers#The_strong_law strong law of large numbers] tells us that as n tends to infinity this will converge to <br />
<br />
<math><br />
G(r) = 0.9\log(1.2r + 1.05(1-r))+0.1\log(1.05(1-r))<br />
</math><br />
<br />
It is a simple calculus problem to show that G(r) is maximized by r = 0.2 with: <br />
G(0.2) = 0.05183. Then e^{0.05183} = 1.0532, showing that our maximum rate of growth is 5.32% as claimed by Peter. <br />
<br />
The attractiveness of the Kelly investment scheme is that, in the long run, any other investment strategy (including those where you are allowed to change your investment proportions at different times) will do less well. "In the long run and less well" means more precisely that the ratio of your return under the Kelly scheme and your return under any other strategy will tend to infinity.<br />
<br />
Thorp had a very good experience in the stock market, which is described very well by Gaeton Lion in his excellent [http://www.amazon.com/gp/product/customer-reviews/0809046377/ref=cm_cr_dp_pt/103-8647004-5865443?%5Fencoding=UTF8&n=283155&s=books review] of ''Fortune's Formula''. He writes:<br />
<br />
<blockquote> Ed Thorp succeeded in deriving superior returns in both gambling and investing. But, it was not so much because of Kelly's formula. He developed other tools to achieve superior returns. In gambling, Ed Thorp succeeded at Black Jack by developing the card counting method. He just used intuitively Kelly's formula to increase his bets whenever the odds were in his favor. Later, he ran a hedge fund for 20 years until the late 80s and earned a rate of return of 14% handily beating the market's 8% during the period. <br><br><br />
<br />
Also, his hedge fund hardly lost any value on black Monday in October 1987, when the market crashed by 22%. The volatility of his returns was far lower than the market. He did this by exploiting market inefficiencies using warrants, options, and convertible bonds. The Kelly formula was for him a risk management discipline and not a direct source of excess return. </blockquote><br />
<br />
Shannon also made a lot of money on the stock market, but did not use Kelly's formula. In his [http://www.amazon.com/gp/product/customer-reviews/0809046377/ref=cm_cr_dp_pt/103-8647004-5865443?%5Fencoding=UTF8&n=283155&s=books review] Gaeton Lion writes<br />
<br />
<blockquote>Claude Shannon amassed large wealth by recording one of the best investment records. His performance had little to do with Kelly's formula. Between 1966 and 1986, his record beat even Warren Buffet (28% to 27% respectively). Shannon strategy was similar to Buffet. Both their stock portfolios were concentrated, and held for the long term. Shannon achieved his record by holding mainly three stocks (Teledyne, Motorola, and HP). The difference between the two was that Shannon invested in technology because he understood it well, while Buffet did not. </blockquote><br />
<br />
Finally, Thorp provided the following comments for the book cover:<br />
<br />
<blockquote>From bookies to billionaires, you'll meet a motley cast of characters in this highly original, 'outside the box' look at gambling and investing. Read it for the stories alone, and you'll be surprised at how much else you can learn without even trying. --Edward O. Thorp, author of ''Beat the Dealer'' and ''Beat the Market''.</blockquote><br />
<br />
Submitted by Laurie Snell.<br />
<br />
<br />
==Which foods prevent cancer?==<br />
<br />
Which of these foods will stop cancer? (Not so fast)<br><br />
New York Times, 27 September 2005, Sect. F, p. 1<Br><br />
Gina Kolata<br />
<br />
Among other examples, the article includes a [http://www.nytimes.com/imagepages/2005/09/26/science/20050927_CANCER_GRAPHIC.html data graphic] on purported benefits of dietary fiber in preventing colorectal cancer. Early observational studies indicated an association, but subsequent randomized experiments found no effect. <br />
<br />
More to follow.<br />
<br />
<br />
==Slices of risk and the <em>broken heart</em> concept==<br />
[http://www.gloriamundi.org/picsresources/news20050912.pdf How a Formula Ignited Market That Burned Some Big Investors],<br />
Mark Whitehouse, The Wall Street Journal, September 12, 2005.<br><br />
<br />
This on-line article relates how a statistician, David Li,<br />
unknown outside a small coterie of finance theorists, helped change the world of investing. <br />
<br />
The article focuses on a event last May when General Motors Corp's debt<br />
was downgraded to junk status, causing turmoil in some financial markets.<br />
The article gives a nice summary of the underlying financial instruments known<br />
as credit derivatives -<br />
investment contracts structured so their value depends on the behavior of some other thing or event -<br />
with exotic names like <br />
[http://en.wikipedia.org/wiki/Collateralized_debt_obligations collateralized debt obligations] and [http://en.wikipedia.org/wiki/Credit_default_swap credit-default swaps].<br />
<br />
The critical step is to estimate the likelihood that many of the companies <br />
in a pool of companies would go bust at once. <br />
For instance, if the companies were all in closely related industries,<br />
such as auto-parts suppliers, they might fall like dominoes after a catastrophic event.<br />
Such a pool would have a 'high default correlation'.<br />
<br />
In 1997, nobody knew how to calculate default correlations with any precision. <br />
Mr. Li's solution drew inspiration from a concept in actuarial science known as the <br />
<em>broken heart</em> syndrome - people tend to die faster after the death of a beloved spouse. <br />
Some of his colleagues from academia were working on a way to predict this<br />
death correlation, something quite useful to companies that sell life insurance and joint annuities.<br />
He says:<br />
<blockquote><br />
Suddenly I thought that the problem I was trying to solve was exactly like the problem these<br />
guys were trying to solve,.<br />
Default is like the death of a company, so we should<br />
model this the same way we model human life."<br />
</blockquote><br />
<br />
This gave him the idea of using [http://en.wikipedia.org/wiki/Copula_%28statistics%29 copulas], <br />
mathematical functions the colleagues had begun applying to actuarial science. <br />
Copulas help predict the likelihood of various events<br />
occurring when those events depend to some extent on one another. <br />
Until the events last May of this year, one of the most popular copulas for bond pools <br />
was the Gaussian copula, named after <br />
[http://en.wikipedia.org/wiki/Carl_Friedrich_Gauss Carl Friedrich Gauss], a 19th-century German statistician. <br />
<br />
===Further reading===<br />
* The [http://www.gloriamundi.org/picsresources/news20050912.pdf on-line article] gives more details about what went wrong in the financial markets in May and the search for a more appropriate copula to capture better the <em>broken heart</em> syndrome between companies.<br />
* [http://en.wikipedia.org/wiki/Wikipedia Wikipedia] is a very worthwhile on-line resource for definitions of technical words, such as [http://en.wikipedia.org/wiki/Copula_%28statistics%29 copula].<br />
<br />
Submitted by John Gavin.<br />
<br />
<br />
==Learning to speak via statistics and graph theory==<br />
<br />
[http://education.guardian.co.uk/tefl/teaching/story/0,15085,1576100,00.html Computer learns grammar by crunching sentences], Max de Lotbinière September 23, 2005, [http://www.guardianweekly.co.uk/ Guardian Weekly].<br><br />
[http://www.cornellsun.com/vnews/display.v/ART/2005/09/09/432118a84f6af Profs’ New Software ‘Learns’ Languages], Ben Birnbaum, 9 Sep 2005, Cornell Daily Sun.<br />
<br />
A language-learning robot may sound like science fiction but new software, developed by Cornell University psychology professor Shimon Edelman, with colleagues Zach Solan, David Horn and Eytan Ruppin from Tel Aviv University in Israel, is well on the way to constructing a computer program that can teach itself languages and make up its own sentences, the developers' claim.<br />
<br />
Unlike previous attempts at developing computer algorithms for language learning - "Automatic Distillation of Structure," or "ADIOS" for short - discovers complex patterns in raw text by repeatedly aligning sentences and looking for overlapping parts.<br />
Once it has derived a language's rules of grammar,<br />
it can then produce sentences of its own, simply from blocks of text in that language.<br />
<br />
It has been evaluated on artificial context-free grammars with thousands of rules, <br />
on natural languages as diverse as English and Chinese, <br />
on coding regions in DNA sequences and on protein data correlating sequence with function. <br />
<br />
Edelman comments:<br />
<blockquote><br />
Adios relies on a statistical method for pattern extraction and on structured generalisations <br />
- the two processes that have been implicated in language acquisition.<br />
Our experiments show that Adios can acquire intricate structures <br />
from raw data including transcripts of parents' speech directed at two- or three-year-olds.<br />
This may eventually help researchers understand how children, <br />
who learn language in a similar item-by-item fashion, and with little supervision, <br />
eventually master the full complexity of their native tongue.<br />
</blockquote><br />
<br />
[http://plus.maths.org/latestnews/may-aug05/adios/ Plus Magazine's website]<br />
offers a more logical explanation:<br />
<blockquote><br />
The ADIOS algorithm is based on statistical and algebraic methods performed on one of the most basic and versatile objects of mathematics - the graph.<br />
Given a text, the program loads it as a graph by representing each word by a node, or vertex, and each sentence by a sequence of nodes connected by lines. A string of words in the text is now represented by a path in the graph. <br><br />
<br />
Next it performs a statistical analysis to see which paths, or strings of words, occur unusually often. <br />
It then decides that those that appear most frequently - called "significant patterns" - <br />
can safely be regarded as a single unit<br />
and replaces the set of vertices in each of these patterns by a single vertex, <br />
thus creating a new, generalised, graph.<br><br />
<br />
Finally, the program looks for paths in the graph which just differ by one vertex. <br />
These stand for parts of sentences that just differ by one word (or compound of words) like "the cat is hungry" and "the dog is hungry". <br />
Performing another statistical test on the frequency of these paths, the program identifies classes of vertices, or words, that can be regarded as interchangeable, or equivalent. <br />
The sentence involved is legitimate no matter which of the words in the class - in our example "cat" or "dog" - you put in.<br><br />
<br />
This last step is then repeated recursively.<br><br />
</blockquote><br />
<br />
[http://plus.maths.org/latestnews/may-aug05/adios/ The website] uses graphs to illustrate some examples and it finishes with some reassuring words:<br />
<blockquote><br />
All this doesn't mean, of course, that the program actually "understands" what it's saying. It simply knows how to have a good go at piecing together fragments of sentences it has identified, in the hope that they are grammatically correct. So if, like me, you're prone to swearing at your computer, you can safely continue to do so: it won't answer back for a long while yet.<br />
</blockquote><br />
<br />
===Further reading===<br />
The [http://adios.tau.ac.il/ ADIOS homepage] offers an overview and more detailed description of the program.<br />
<br />
Submitted by John Gavin.<br />
<br />
==Understanding probability==<br />
<br />
Understanding Probability:Chance rules in everyday life<br><br />
Cambridge University Press 2004<br><br />
Henk Tijms<br />
<br />
Hank Tijms is Professor in Operation Research at the Vrije University in Amsterdam. This book is based on his earlier Dutch book “Spelen met Kansen.” <br />
<br />
The aim of this book is to show how probability applies to our everyday life in a way that your Uncle George could understand even if he has forgotten much of his high school math. Tijms does not try to avoid mathematics but only to postpone the formal math until the reader has seen the many applications of probability in the real world, how much fun it is, and learned to work problems and when he can’t work one how to get the answer by simulation. He learns all this in part I of the book and then he learns the more formal math in Part II.<br />
<br />
In Chapter 1 Tijms asks the reader to think about problems with surprising answers in the spirit of Susan Holmes “[http://www-stat.stanford.edu/~susan/surprise/ Probability by Surprise]” including the birthday problem and the Monty Hall problem. Readers are on their own to try to solve one or more of the problems but promised that they will see the solutions later in the book. <br />
<br />
Chapter 2 deals with the law of large numbers and introduces the concept of simulation. This theorem is explained and illustrated by problems related, for example, to coin tossing, random walks and casino games. Expected value is introduced in an informal way to be defined more carefully later in the book. For the reader who is not frightened by mathematical formulas, Tijms includes a discussion of the Kelly betting system with a footnote saying that this paragraph can be skipped at first reading. This is a fascinating topic that is widely applied in gambling and stock investment but rarely appears in a probability book.<br />
<br />
In Chapter 3 the author returns to previous problems such as the birthday problem and gambling systems and solves them first by simulation and then by mathematics. <br />
<br />
In this chapter Tijms describes Efron’s bootstrap method and uses it to solve a number of problems including a hypothetical clinical trial and to test if the famous 1970 draft lottery during the Vietnam War was fair. Again the bootstrap method has wide application but rarely occurs in an elementary probability or statistics book.<br />
<br />
Chapter 4 describes the binomial, Poisson, and hypergeomtric distributions and how to use them in solving problems such as the famous hat check problem, and a variety of interesting lottery questions. The Poisson process is discussed but again with the footnote that novice readers might want to read this at a later time.<br />
<br />
Chapter 5 is mainly about Center Limit Theorem and its many applications especially to statistics. <br />
<br />
Chapter 6 introduces Chance trees and Bayes’s rule. The tree method is used to explain a variety of problems including the Monty Hall Problem and the false-positive paradox. <br />
<br />
This is a brief description of the first six chapters which constitute Part I of the book. Now the fun is over. Part 2 called “Essentials of probability” looks like the traditional first chapters in a standard probability book. But the reader has already found how exciting probability is, has a good intuitive idea of the basic concepts and has worked many of the interesting problems at the end of each chapter either using math or simulation. For some students this might allow them to actually enjoy Part 2. But your Uncle George may want to quit while they are ahead. <br />
<br />
Tijms writes with great clarity and his enthusiasm for probability in the real world is contagious. We were delighted to see, as acknowledged in the preface, that Tijms included several of the more interesting problems discussed in Chance News, often going well beyond what we had said in our discussion of the problem. <br />
<br />
This book presents a completely new way to go about teaching a first course in probability and we think those who teach such a course should consider trying it out.<br />
<br />
===Discussion===<br />
<br />
(1) In the days of Basic we required all students to learn Basic in their first math course so we could assume that students could write programs to simulate probability problems and so me made heavy use of simulation as suggested in this book. The author uses Pascal in his book. What present language do you think is easiest for a student with no computing experience to learn?<br />
<br />
We asked Professor Tijms what the situation was in math departments in Europe and he replied:<br />
<br />
<blockquote>In math departments of universities and polytechnic schools in Europe students learn to write computer programs. In my university they still learn to program in Java and C++ ( in previous days Pascal), but I see in the Netherlands the trend that the instructors think it is sufficient if the students are able to program in Matlab. <br><br><br />
<br />
In ny book I have chosen to formulate the simulation programs in Pascal because of the clarity and the simplicity of the language, though this language is hardly used anymore. The introductory probability course at my university is given before they have learned to program, but this does not prevent them of simulating probability problems by using Excel. In the simulation of many elementary probability problems a random-number generator alone suffices to simulate those problems and so Excel can be used. In the second year they have mastered Matlab, a perfect tool with its excellent graphics to simulate many challenging probability problems ( they really like it, in particular when it concerns problems such as the problems 2.24-2.45 in chapter 2 and the problems 5.11-5.13 in chapter 5). <br />
</blockquote><br />
<br />
<br />
(2) Do you think that probability books should include data to test probability models that are said to describe real world problems? If so name some models that you think would pass such a test and some that you think might not.<br />
<br />
Submitted by Laurie Snell<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Societies worse off when they have God on their side==<br />
<br />
[http://www.timesonline.co.uk/article/0,,2-1798944,00.html Societies worse off when they have God on their side]<br><br />
Timesonline, September 27, 2005<br><br />
Ruth Gledhill<br />
<br />
[http://moses.creighton.edu/JRS/2005/2005-11.html Cross-national correlations of quantifiable societal health with popular religiosity and secularism in the prosperous democracies]<br><br />
Journal of Religion & Society, Vol.7(2005)<br><br />
Gregory S. Paul<br />
<br />
In the Times article we read:<br />
<br />
<blockquote>According to the study, belief in and worship of God are not only unnecessary for a healthy society but may actually contribute to social problems.<br><br><br />
Many liberal Christians and believers of other faiths hold that religious belief is socially beneficial, believing that it helps to lower rates of violent crime, murder, suicide, sexual promiscuity and abortion. The benefits of religious belief to a society have been described as its “spiritual capital”. But the study claims that the devotion of many in the US may actually contribute to its ills. <br />
</blockquote><br />
<br />
Gregory Paul is a dinosaur paleontologist and on an [http://www.abc.net.au/worldtoday/indexes/2005/twt_20050928.htm interview] on Australian ABC radio Paul said that, being a paleontologist, for many years he had to deal with the issue of creationism versus evolutionary science in the U.S and his interest in evolutionary science prompted him to look at whether there was any link between the religiosity of a society and how well that society functions. <br />
<br />
If you look at Paul's article you will find very little technical statistical analysis, for example, he did not carry out a regression analysis. Rather he rests his case on the series of scatterplots.<br />
<br />
Paul describes his data sources as:<br />
<br />
<blockquote>Data sources for rates of religious belief and practice as well as acceptance of evolution are the 1993 Environment I (Bishop) and 1998 Religion II polls conducted by the International Social Survey Program (ISSP), a cross-national collaboration on social science surveys using standard methodologies that currently involves 38 nations. The last survey interviewed approximately 23,000 people in almost all (17) of the developed democracies; Portugal is also plotted as an example of a second world European democracy. Results for western and eastern Germany are combined following the regions' populations. England is generally Great Britain excluding Northern Ireland; Holland is all of the Netherlands. The results largely agree with national surveys on the same subjects; for example, both ISSP and Gallup indicate that absolute plus less certain believers in a higher power are about 90% of the U.S. population. The plots include Bible literalism and frequency of prayer and service attendance, as well as absolute belief in a creator, in order to examine religiosity in terms of ardency, conservatism, and activities. </blockquote><br />
<br />
Here are the countries Paul considered with the abbreviations used on the graphics. <br />
<br />
A = Australia, C = Canada, D = Denmark, E = Great Britain, F = France, G = Germany,<br />
H = Holland, I = Ireland, J = Japan, L = Switzerland, N = Norway, P = Portugal, R = Austria,<br />
S = Spain, T = Italy, U = United States, W = Sweden, Z = New Zealand.<br />
<br />
There seems to be no agreement as to which countries are developed democracies. For example Paul might have included Greece and Belgium, Finland, and others but the data may have determined his choice. Paul comments that he added Portugal as an example of a second world democracy. <br />
<br />
Paul's anaysis of the data includes a series of 9 Figures which are available at the end of the article and are the most interesting part of the study. If you try printing Paul's article you will only get the first of his 9 Figures. When you look at the [http://moses.creighton.edu/JRS/2005/2005-11.html web version] you will still see only Figure 1 but the others can be viewed by selecting the numbers from 2 to 9 on the left side of Figure 1.<br />
<br />
Figure 1 deals with the proportion of people who accept human evolution which is interesting but not as relevant to the welfare of the people as others so we will look at Figure 2.<br />
<br />
[[Image:religion2.png|500px|center|Source:Gregory Paul]]<br />
<br />
Each Figure iprovides 5 separate scatterplots. Ïn Figure 2 we see that the U.S. has largest number--between 6 and 7-- of homicides per 100,000 and Spain has the lowest number with less than 1 homicide per 100,000. We also see that the U.S. has the highest proportion of people, about 25%, who take the bible literally while several countries have less than 10% such people.<br />
<br />
What we cannot do is compare the number of homicides per thousand between those who take the bible literally and those who are agnostics or atheists which is what we would really want to know. Presumably the data did not permit this comparison. <br />
<br />
[[Image:religion3.png|500px|center|Source:Gregory Paul]]<br />
<br />
Figure 3 deals with "14-24 year old suicides per 100,000". Here the U.S. is in about the middle.<br />
<br />
Figure 4 deals with the "under-five mortalities per 1000 births".<br />
<br />
[[Image:religion4.png|500px|center|Source:Gregory Paul]]<br />
<br />
Ignoring Portugal, the U.S. has the highest number of under-five mortalities per 1000 births-- between 7 and--8 while several countries have only 4.<br />
<br />
The other figures can be seen at end of Paul's article. They deal with life expectancy, sexually transmitted diseases, abortion and 15-16 year old pregnancies. Life expectancy is the smallest in the U.S. and for sexually transmitted diseases, abortion and 15-17 year old prenacies the U.S. is at the top of the graphs and in fact these look like outliers.<br />
<br />
Well, this study does not by itself justify the Times hedline: "Societies worse off when they have God on their side." Paul himself would not claim this. He writes:<br />
<br />
<blockquote> This study is a first, brief look at an important subject that has been almost entirely neglected by social scientists. The primary intent is to present basic correlations of the elemental data. Some conclusions that can be gleaned from the plots are outlined. This is not an attempt to present a definitive study that establishes cause versus effect between religiosity, secularism and societal health. It is hoped that these original correlations and results will spark future research and debate on the issue.</block<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div></div>Nano12https://www.causeweb.org/wiki/chance/index.php?title=Chance_News_9&diff=1547Chance News 92005-11-05T09:34:16Z<p>Nano12: /* Quotation */</p>
<hr />
<div>==Quotation==<br />
Å quotation will be added here.<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Forsooth==<br />
Forsooth items should be added here.<br />
==Supreme Court Nominee Alito: Statistics Misleading?==<br />
An [http://www.salon.com/politics/war_room/2005/10/31/jury/index.html article] in Salon.com for October 31 discusses the first-degree murder trial, Riley v. Taylor. The defendant Riley was African-American; at the trial, the prosecution used its peremptory challenges to eliminate all three of the African-Americans on the jury panel. In the same county that year, there were three other first-degree murder trials, and in every one of those cases all of the African-American jurors were struck.<br />
<br />
A majority of the judges on the appeals court thought that there was evidence that jurors were struck for racial reasons. According to them, a simple calculation indicates that there should have been five African-American jurors amongst the forty-eight that were empanelled. However, there were none. To these judges, this was clear evidence of racial motivaion in the striking of such jurors.<br />
<br />
Judge Alito dissented. He called the majority's analysis simplistic, and stated that although only 10% of the U.S. population is left-handed, five of the last six people elected president of the United States were left-handed. He asked rhetorically whether this indicated bias against right-handers amongst the U.S. electorate.<br />
<br />
The majority responded that there is no provision in the Constitution that protects persons from discrimination based on whether they are right-handed or left-handed, and that to compare these cases with the handedness of presidents ignores the history of racial discrimination in the United States.<br />
<br />
===Questions===<br />
<br />
1) Assuming that Judge Alito is correct about the proportion of left-handers in the U.S. population, what is the probability that five of the last six presidents elected would be left-handed?<br />
<br />
2) Is Judge Alito's comparison biased by the fact that he chose just the last six presidents? Presumably he believed that the president just before this group was right-handed, otherwise he would have included him in the sample and said "six of the last seven presidents." What is the relevant statistic?<br />
<br />
3) When the decision came down in 2001, the last six people elected president were George W. Bush, Clinton, George H. W. Bush, Reagan, Carter and Nixon. Of these, Clinton and George H. W. Bush were left-handed. Ford, who was left-handed, was not elected president (or even vice-president); he became president upon the resignation of Richard Nixon. Reagan may have been left-handed as a child, but he wrote right-handed so his case isn't clear; the Reagan Presidential Library [http://www.reagan.utexas.edu/archives/reference/facts.html says] that he was "generally right-handed." Judge Alito may have been confused, including on his list Ford (who was not elected) and George W. Bush (who is not left-handed, although his father is), as well as Reagan. The other left-handed presidents were Truman and Garfield. Hoover is found on some lists of left-handed presidents, but according to the Hoover Institution, he was not left-handed. How does this information affect Alito's argument?<br />
<br />
4) Suppose that 5/48 of the jury pool were African-American. What is the probability that no juror amongst the 48 selected would have been African-American? How does this compare with the actual statistics of left-handed presidents? Does the same objection apply to this case as might apply to Alito's example?<br />
<br />
5) What is your opinion? Is there clear statistical evidence of racial bias in the use of peremptory challenges in this county?<br />
<br />
6) What does it say about our judiciary that Judge Alito could get his facts as wrong as he did, and that none of the judges in the majority caught the errors?<br />
<br />
Contributed by Bill Jefferys<br />
<br />
==item2==<br />
Replace item2 by the name of your article.</div>Nano12https://www.causeweb.org/wiki/chance/index.php?title=Chance_News_8&diff=1546Chance News 82005-11-05T09:34:13Z<p>Nano12: /* Forsooth */</p>
<hr />
<div>Oct 15 to Oct 30<br />
<br />
==Quotation==<br />
<blockquote>One more fagot of these adamantine bandages, is, the new science of Statistics. It is a rule, that the most casual and extraordinary events -- if the basis of population is broad enough -- become matter of fixed calculation. It would not be safe to say when a captain like Bonaparte, a singer like Jenny Lind, or a navigator like Bowditch, would be born in Boston: but, on a population of twenty or two hundred millions, something like accuracy may be had. Ralph Waldo Emerson Fate</blockquote><br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Forsooth==<br />
Here's another Forsooth from the October issue of RSS News.<br />
<blockquote>Your'e more likely to die in a fire in Strathclyde than anywhere else in the country</blockquote><br />
<br />
<div align="right">BBC1 mews bullietin<br><br />
11 May 2005</div><br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==The Poisson distribution and the Supreme Court==<br />
The Poisson distribution and the Supreme Court<br><br />
''Journal of the American Statistical Association'' 31, no. 195 ,(1936), 376-80<br><br />
W. Allen Wallis<br />
<br />
Supreme Court Appointments as a Poisson distribution<br><br />
''American Journal of Political Science'', 26, No.1, February 1982<br><br />
S. Sidney Ulmer<br />
<br />
This is not current news, but since Supreme Court appointments are in the news we felt that these articles might make an interesting class discussion.<br />
<br />
In 1936 statistician Allen Wallis suggested that a Poisson distribution can approximate the number of U.S. Supreme Court appointments in a given year. In his Table 1 Wallis provided the number appointed in each year over the intervals with different numbers of Justices on the Supreme Court: 1790-1806 (6) 1807-1836 (7), and 1837-1932 (9). Actually there were 10 in the years 1963 to 1967 which Wallis called "negligible exceptions."<br />
<br />
[[Image:wallis1.png|500px|center]]<br />
<br />
Wallis then restricts himself to the years 1837-1932 and finds that a Poisson distribution with mean .5 can approximate the number of court appointments in a year. His results are shown in his Figure II:<br />
<br />
[[Image:wallis2.png|500px|center]]<br />
<br />
In his article, Sidney Ulmer updated the data to 1980 and also includes data from the early Supreme Courts with 6 and 7 members. Thus his data covers the years 1790--1980. His Table 1 compares the actual number of appointments in a year with the expected number of appointments assuming a Poisson distribution with mean 5.13.<br />
<br />
[[Image:ulmer1.png|500px|center]]<br />
<br />
In his Table II Ulmer limits the data to the 9 member Supreme Courts: 1837 to 1862 and 1869-1980).<br />
<br />
[[Image:ulmer2.png|500px|center]]<br />
<br />
Testing the goodness of fits, Ulmer argues that the fit with the varying size Supreme Courts is just as good as with fixed size Supreme Courts.<br />
<br />
===DISCUSSION===<br />
<br />
(1) What is the probability that a President will make 2 or more appointments to the Supreme Court during a 4-year term? What is the probability a President makes no appointments during a 4-year term? Has this ever happened?<br />
<br />
(2) Do you agree with Ulmer that there is no reason to limit the data to years with the Supreme Court is the same size?<br />
<br />
(3) Obtain the data needed to update Ulmer's results to today and provide Tables that correspond to Ulmer's Tables 1 and 2. Add your Tables to this Chance News and make your data available to make it easier to update this in future years.<br />
<br />
Contributed by Laurie Snell<br />
<br />
==Possible Cancer Cluster in Connecticut==<br />
Pratt Agrees to Increase Funding for Brain Cancer Study <br><br />
''The Associated Press''<br><br />
October 11, 2005<br><br />
Stephen Singer<br><br />
<br />
<br />
In a case that seems eerily familiar to the leukemia cancer cluster made famous by the book and movie, ''A Civil Action'', researchers are trying to determine whether or not a cancer cluster exists among workers at Pratt & Whitney, a company that manufactures jet engines. Over one hundred former or current Pratt & Whitney employees have been identified as having a relatively rare type of fatal brain tumor known as glioblastoma multiforme, which strikes 3 people per 100,000 every year. Many of these workers have been exposed to metals and chemical substances, including TCE (trichloroethylene), which is an engine degreaser. TCE is the same carcinogenic chemical that was dumped in the 1960’s and 1970’s by the chemical company, WR Grace, in Woburn, MA, and that was found to have contaminated the drinking water in two of the town’s wells. <br><br />
<br />
<br />
Prior to the recent announcement that the funding is being increased from $6 million dollars to $12 million dollars, this medical study was already being described as the largest occupational health study ever conducted. It covers 250,000 people who worked at any of the seven Connecticut Pratt & Whitney plants from 1952 to 2001. So far, at least 125 cases of brain cancer have been documented, according to the lawyer who represents dozens of individuals and family members.<br><br />
<br />
<br />
The study falls under the auspices of the Connecticut Department of Public Health. However, due to the overwhelming cost and scope of the study, Pratt & Whitney is funding the project. Since Pratt is paying for the study, they chose the researchers, a team from the University of Pittsburgh. The project began three years ago, and the results are expected to be available between 2007 and 2009.<br><br />
<br />
<br />
In the meantime, this case faces many of the obstacles common in the quest to establish whether or not a cancer cluster exists, such as proving causation, the fact that it can take a long time (sometimes 5-40 years) after exposure for true problems to show up, and finding the people who were exposed & convincing them to participate in the study. Additionally, there are legal difficulties for the families involved, including Connecticut’s statute of limitations laws, the length of time it takes investigators to reach a conclusion, the cost of litigation, and the “deep pockets” of a company like Pratt & Whitney.<br><br />
<br />
<br />
This case study provides a current example of an ongoing investigation into a possible cancer cluster. Will it ultimately be found to be a coincidence cluster or proven to be a true cancer cluster? Does it make sense that the researchers are including in the study everyone who worked at Pratt over a fifty year period, even those who only worked there for a brief time period and those who were not directly exposed to toxic substances (i.e. office workers)? Could the researchers possibly have an unconscious bias in favor of the company that is funding their research? If the company doesn’t fund the research, then who should? Is there some other way to structure such investigations, so that the company involved pays for the study, but is not allowed to choose the researchers and directly fund them?<br><br />
<br />
<br />
'''Further Reading'''<br><br />
<br />
• “Rare Cancer Found in Workers”, ''The New York Times'', March 10, 2002, Jane Gordon<br><br />
• “Scientist: Pratt Commits to Cancer Study”, ''The Hartford Courant'', May 19, 2005<br><br />
• “Participation in Cancer Study at Pratt Lagging”, ''The Hartford Courant'', October 12, 2005, Paul Marks<br><br />
• ''The New Haven Advocate'' has had more than a dozen articles that explain the working conditions at Pratt & Whitney, and also chronicle the history & progression of this case. These articles have been investigated and written primarily by Carole Bass, Associate Editor. A few of the articles are listed below. <br> <br />
-“Worked to Death”, August 2, 2001, Carole Bass & Camille Jackson<br><br />
-“Talking Cure”, October 28, 2004, Dave Goldberg<br><br />
-“Time’s Not on Their Side”, January 20, 2005, Carole Bass<br><br />
-“The Brains Behind the Brain”, October 20, 2005, Carole Bass <br><br />
For the early New Haven Advocate articles (i.e., 2001-2002) on this subject, go to http://old.newhavenadvocate.com/workedtodeath/index.html<br> <br />
For the articles since 2002, go to <br><br />
http://www.newhavenadvocate.com and search for Pratt & Whitney.<br><br />
<br />
Submitted by Josephine Rodriguez.<br />
<br />
==A record powerball lottery jackpot==<br />
<br />
On Saturday Oct 22, 2005 the powerball lottery had a record powerball jackpot of 340 million dollars. <br />
<br />
When you buy a ticket for this lottery, you specify five distinct numbers from 1 to 55, which we call basic numbers and one number from 1 to 42 called the bonus number. To win the Jackpot your 5 basic numbers and your bonus number must agree with a random choice of 5 basic numbers and one bonus number chosen by the lottery officials. The number of possible tickets is:<br />
<br />
<center><math>{55 \choose 5} 42 = </math> 146,107,962</center><br />
<br />
Thus if you buy a single ticket, the probability of having a winning jackpot ticket is<br />
<br />
<center> <math>{1} \over {146107962}</math> = .000000006844...</center><br />
<br />
The powerball website and the media expresses this by saying that the odds that you have a winning jackpot ticket is 1 in 146,107,962. <br />
<br />
Whenever there is a record jackpot, the news writers look for suggestions for other rare events that might be more familiar to its readers. <br />
<br />
Our own favorite was suggested by Fred Hoppe: if you toss a coin 27 times your chance of getting 27 heads in a row is greater than your chance of having a winning jackpot ticket when you buy a single ticket. (<math> 2^{27} = 134217728</math> and so there are 134,217,728 possible sequences of heads and tails and only 1 has all heads.)<br />
<br />
In an article for the ''Omaha World-Herald'' Oct 18, 2005 , Robynn Tysver writes:<br />
<br />
<blockquote> You have a greater chance of getting killed by lightning than winning this week's 340 million Powerball jackpot. You also have a greater chance of drowning in a bathtub. The lifetime odds of getting killed by lightning are one in 56,439, and the lifetime odds of dying while in or falling into a bathtub are one in 10,582, according to the National Safety Council. <br />
</blockquote><br />
<br />
These are not even in the ballpark. The ''Minneapolis Star Tribune'' consulted mathematicians David Bressoud and Douglas Arnold who contributed the following:<br />
<br />
According to Arnold you have a seven times better chance of becoming a saint. And Bressoud notes that you're six times more likely to get elected president of the United States. But they also provide the following more interesting estimates:<br />
<br />
<blockquote>Bressoud: "If you buy 10 tickets a week, every week, it would take you 280,000 years before you could expect to win."<br><br><br />
<br />
Arnold: "If you were to select a group of Powerball numbers every minute for 138 years, you would have about a 50 percent chance of picking the winning Powerball ticket." <br><br><br />
<br />
It is not clear what Bressoud means by "expect to win". We can check this by a simple calculation (simple for Mathematica). Let q(n) be the probability that you if you buy n tickets you fail to get a winning jackpot ticket . Then:<br />
<br />
<center> <math> \left(\frac{146107961}{146107962}\right) ^n = q(n) </math></center><br />
<br />
The average number of weeks in a year is 52.177457 so If you buy 10 tickets a week, every week for 280,000 years you will buy about 146,097,000 tickets. Using this number for n in our formula we find that you have about a 37% chance of not getting a winning lottery ticket or a 63% chance of getting one. We would not "expect to win" with a 63% chance of winning but others may. Using our formula for q(n) we find that if we buy 10 tickets a week, every week for 830,000 years you will have about a 95% chance of getting at least one winning lottery ticket which seems to us more appropriate for expecting to win. <br />
<br />
Consider now Arnold's example. Our colleague Dana Williams found that you need to buy a ticket for about 101 million lottery offerings to have about a 50% chance of getting at least one winning lottery ticket. There are an average of 525,946.766 minutes in a year. Dividing 101 million by this number gives 192.035. Thus Arnold's 138 years should be 192 years.<br />
<br />
We asked Professor Arnold about this and he replied:<br />
<br />
<blockquote> That number, which was quoted in the ''Star Tribune'' was an off-the-top-of-my-head calculation made when the reporter called me on<br />
the phone with no warning. Right ballpark, but not very accurate. Later I redid the calculation carefully.</blockquote><br />
<br />
Arnold's computations were similar to ours but he used a greater accuracy for the number of independent lotteries you have to buy to have a 50% chance of choosing the jackpot numbers at least once. His answer to this was 101,274,322. Using this, Arnold's estimate for the number of years, buying a ticket every minute, to have a 50% chance of winning a jackpot is193 years instead of our estimate of 192 years.<br />
<br />
Arnold said that he also estimated the expected value of a $1 ticket. To do this he needed an estimate for the number of tickets sold. He was told that a reasonable estimate was 106 million. In calculating the expected value of a $1 ticket he used the cash value of 164.4 million dollars instead of the annuity payout of 340 million dollars. He also took into account the possibility of having to share the jackpot. Doing this he got an expected value of exactly $1, just the price of the ticket. He commented that if he took into account the taxes the expected value would be more like 80 cents making even this lottery an unfavorable event.<br />
<br />
The news writers also gave a lot of coverage of Senator Gregg (Chairman of the Senate Budget Committee) winning $853,492 for getting the second highest prize: getting the 5 basic numbers correct but note the bonus number. Normally the prize for getting this is $200,000 cash but Gregg was the beneficiary of recent change in the powerball lottery. <br />
<br />
The powerball officials have found that increasing the size of the jackpot can increase the ticket sales because of the public's interest in large jackpots. They do this by increasing the number of possible basic numbers. When they started in 1992, to get the jackpot you had to get the 5 basic numbers chosen from 45 numbers and the 1 bonus number chosen from 45 number correct. Here are the changes so far<br />
<br />
<center><br />
1992 5 of 45 1 of 45<br><br />
1997 5 or 49 1 of 42<br><br />
2002 5 of 55 1 of 42<br><br />
2005 5 of 55 1 of 42<br><br />
</center><br />
<br />
While the lottery officials want to have higher jackpots, they also do not want too long a period between jackpots. Normally the increase in the size of the lottery, when no one wins the jackpot, is determined by the amount taken in in this unsuccessful drawing. This was recently changed so that, when a new record jackpot occurs and no-one wins it, at most 25 million dollars are added to the Jackot until someone wins the jackpot. The money save by this is added to the second prize.<br />
<br />
When the 340 million jackpot was won, 49 players had the five basic numbers correct but not the bonus numbers. For these winners the $200,000 prize had 653,492 added to their prize so they each won $853,492. If they chosen the Powerball play option for an extra $1 their $200,000 would have been multiplied by 2,3,4, or 5 with equal probabilities. Thus if Gregg had chosen the Powerball play option, and been lucky, he would have won 1,653,492 dollars that he could add to his 15 or so million dollars he has in stocks. <br />
<br />
===DISCUSSION===<br />
<br />
(1) Do you think it is fair to advertise the lottery prize as 340 million when the cash prize is only 164.4 million?<br />
<br />
(2) What is the probability of winning the second prize?<br />
<br />
(3) Assuming that the estimate 106 million for the number of tickets sold find the expected number of second prize winners.<br />
<br />
==Mammograms Validated as Key in Cancer Fight==<br />
<br />
The ''New York Times'' [http://www.nytimes.com/2005/10/27/health/27breast.html reported] on October 27, 2005 on a new National Cancer Institute study that attributed a significant decrease in the death rate from breast cancer to mammogram screening tests. The study, published in the New England Journal of Medicine, found that from 28% to 65% of the sharp 24% decrease in breast cancer death rates from 1990 to 2000 was due to screening; the remainder was attributed to new drugs used to treat the disease.<br />
<br />
Prior to this study, the value of mammogram screening had been disputed, for several reasons. In the general population, the test results in a large proportion number of false positives, about 90%. Thus, many women who are cancer-free are subjected to unnecessary procedures. Also, approximately 30% of cancers that are detected and treated would not have progressed significantly. Unfortunately, it isn't possible to distinguish between these so-called ''indolent'' cancers and those that become life-threatening, so it is routine practice to treat them all.<br />
<br />
The new study suggests that the benefits of routine mammography are more certain than earlier believed, according to Don Berry, Chairman of the biostatistics department of M. D. Anderson Cancer Center, in Houston, Texas, and the lead author of the paper. He said that the new study for the first time properly separates the effects of therapy and screening. Nonetheless, he cautioned that mammography does pose risks, and recommended that women be counselled before screening.<br />
<br />
Contributed by Bill Jefferys<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div></div>Nano12https://www.causeweb.org/wiki/chance/index.php?title=Chance_News_7&diff=1545Chance News 72005-11-05T09:34:10Z<p>Nano12: /* Forsooth */</p>
<hr />
<div>Sept 26 2005 to Oct 15 2005<br />
==Quotation==<br />
<blockquote><br />
While writing my book [Stochastic Processes] I had an argument with Feller [Introuction to Probability Theory and its Applications]. He asserted that everyone said "random variable" and I asserted that everyone said "chance variable." We obviously had to use the same name in our books, so we decided the issue by a stochastic procedure. That is, we tossed for it and he won. </blockquote><br />
<br />
<p align = right> Joe Doob<br><br />
[http://www.dartmouth.edu/~chance/Doob/conversation.html Statistical Science]<br><br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Forsooth==<br />
<br />
Peter Winkler suggested our first forsooth.<br />
<br />
<blockquote>Texas beats Ohio State in their opening game <br />
of the season (Saturday Sept 10 2002). The sportscasters (legendary Brent Musburger on play-by-play or Gary Danielson on analysis) observed that of the 14 teams who have <br />
previously played in the championship game (at the end of each season) 5 <br />
have suffered an earlier defeat. "Thus," they conclude, "Ohio State can <br />
still make it to the championship game, but their chances are now less <br />
than 50%."</blockquote><br />
<br />
===Discussion===<br />
<br />
What is wrong with this?<br />
----<br />
Here are forsooths from the September 2005 issues of RSS NEWS<br />
<br />
<blockquote>'Big ticket quiz' at the start of Wimbledon:<br><br><br />
Q. How many punnets (a small light basket or other container for fruit or vegetables) of strawberries are eaten each day during the Wimbledon tournament?<br><br />
Is it (a) over 8,000, (b) over 9,000 or (c) over 10,000?</blockquote><br />
<br />
<div align="right">BBC radio 5<br><br />
20 June 2005</div><br />
<br />
<blockquote>Waiting time for foot surgery down by 500%</blockquote><br />
<br />
<div align="right">Evening News (Edinburgh)<br><br />
5 July 2005</div><br />
<br />
The next two forsooths are from the October RSS news.<br />
<br />
<blockquote>In 1996-8 when the number attending university was static, the participation of women was also static, but male participation fell.</blockquote><br />
<br />
<div align="right">The Times Higher<br><br />
21 January 2005</div><br />
<br />
<blockquote>[On the subject of congestion on the London Underground..] 'Last year 976 million of us used the tube...'</blockquote><br />
<br />
<div align="right">BBC London News<br><br />
19 May 2005</div><br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Fortune's Formula==<br />
<br />
''Fortune's Formula: Wanna Bet?''<br><br />
''New York Times Book Section'', September 25, 2005<br><br />
David Pogue<br />
<br />
This must be the kind of review that every Science writer dreams of. Pogue ends his review with:<br />
<br />
<blockquote> ''Fortune's Formula'' may be the world's first history book, gambling primer, mathematics text, economics manual, personal finance guide and joke book in a single volume. Poundstone comes across like the best college professor you ever had, someone who can turn almost any technical topic into an entertaining and zesty lecture. But every now and then, you can't help wishing there were some teaching assistants on hand to help.</blockquote><br />
<br />
The author William Poundstone is a science writer who has written a number of very successful science books. His book, ''Prisoner's dilemma: John von Neumann, game theory and the puzzle of the bomb'', was written in the style of this book. Indeed Helen Joyce, in her review of this book in Plus Magazine writes:<br />
<br />
<blockquote>This book is a curious mixture of biography, history and mathematics, all neatly packaged into an entertaining and enlightening read. </blockquote><br />
<br />
Poundstone describes himself as a visual artist who does books as a "day job.". You can learn about his art work [http://www.uiowa.edu/~iareview/tirweb/feature/poundstone/interview2.htm here].<br />
<br />
''Fortune's Formula'' is primarily the story of Edward Thorp, Claude Shannon, and John Kelly and their attempt to use mathematics to make money gambling in casinos and on the stock market. None of these did their graduate work in mathematics. Thorp and Kelly got their Phd's in physics and Shannon in Genetics. <br />
<br />
In the spring of 1955, while a graduate student at UCLA, Thorp joined a discussion on the possiblity of making money from roulette. Thorp suggested that they could taking advantage of the fact that bets are still accepted for a few second after the croupier releases the ball, and in these seconds, he could estimate what part of the wheel the ball would stop. <br />
<br />
Thorp did not pursue this and in 1959 became an instructor in mathematics at M.I.T. Here he became interested in blackjack and developed his famous card counting method for wining at blackjack. He decided to publish his method in the most prestigious journal he could find and settled on ''Proceedings of the National Academy of Sciences''. For this he needed to have a member of the Academy submit his paper. The only member in the math department was Shannon so he had to persuade him of the importance of his paper. Shannon not only agreed but in the process became fascinated by Thorp's idea for beating roulette. He agreed to help Thorp carry this out. They built a roulette machine in Shannon's basement. It worked fine there in trial runs but not so well in the casino so they did not pursue this method of getting rich. <br />
<br />
Of course Thorp is best known for showing that blackjack is a favorable game and giving a method to exploit this fact. Shannon is best known for his work in information theory. Kelly is known his method for gambling in a favorable game. This plays a central role in Poundstone's book and is probably why Pogue felt that it would help if he had a teaching assistant. Poundstone tries to explain Kelly's work in many different ways but what he really needed to understand it is an example but this required too many formulas for a popular book. So we shall include an example from Chance News 7.09. <br />
<br />
Writing for Motley Fool, 3 April 1997 Mark Brady complained about the inumeracy of the general public and gave a number of examples including this one:<br />
<br />
<blockquote> Fear of uncertainty and innumeracy are synergistic. Most people cannot do the odds. What is a better deal over a year? A 100% safe return with 5 percent interest or a 90 percent safe return with a 20 percent return. For the first deal, your return will be 5% percent. For the second, your return will be 8%. Say you invest $1000 10 times. Your interest for the 9 successful deals will be 9000 x 0.2 or 1800. Subtract the 1000 you lost on the 10th deal and you get a $800 return on your original $10,000 for 8 percent.</blockquote><br />
<br />
Peter Doyle suggested that a better investment strategy in this case is:<br />
<br />
Faced with a 100 percent-safe investment returning 5 percent and a 90 percent-safe investment returning 20%, you should invest 20% of your funds in the risky investment and 80% in the safe investment. This gives you an effective return of roughly 5.31962607969968292 percent. <br />
<br />
Peter is using a money management system due to J. L. Kelly (1956: "A new interpretation of information rate," ''Bell System Technical Journal'', '''35'''). Kelly was interested in finding a rational way to invest your money faced with one or more investment schemes, each of which has a positive expected gain. He did not think it reasonable to try simply to maximize your expected return. If you did this in the Motley Fools example as suggested by Mark Brady, you would choose the risky investment and might well lose all your money the first year. We will illustrate what Kelly did propose in terms of Motley Fools example. <br />
<br />
We start with an initial capital, which we choose for convenience to be $1, and invest a fraction r of this money in the gamble and a fraction 1-r in the sure-thing. Then for the next year we use the same fractions to invest the money that resulted from the first year's investments and continue, using the same r each year. Assume, for example, that in the first and third years we win the gamble and in the second year we lose it. Then after 3 years our investment returns an amount f(r) where: <br />
<br />
<math><br />
f(r) = (1.2r + 1.05(1-r))(1.05(1-r))(1.2r + 1.05(1-r)). <br />
</math><br />
<br />
After n years, we would have n such factors, each corresponding to a win or a loss of our risky investment. Since the order of the terms does not matter our capital will be: <br />
<br />
<math><br />
f(r,n) = (1.2r + 1.05(1-r))^W(1.05(1-r))^L<br />
</math><br />
<br />
where W is the number of times we won the risky investment and L the number of times we lost it. Now Kelly calls the quantity:<br />
<br />
<math><br />
G(r) =\lim_{n \to \infty }\frac{\log(f( r,n)} {n}<br />
</math> <br />
<br />
the exponential rate of growth of our capital. In terms of G(r) our capital should grow like <math> e^{G(r)} </math>. In our example: <br />
<br />
<math><br />
\log(\frac{f(r,n)}{n}) = \frac{W}{n}\log(1.2r + 1.05(1-r)) + \frac{L}{n}\log(1.05(1-r))<br />
</math> <br />
<br />
Since we have a 90% chance of winning our gamble, the [http://en.wikipedia.org/wiki/Strong_law_of_large_numbers#The_strong_law strong law of large numbers] tells us that as n tends to infinity this will converge to <br />
<br />
<math><br />
G(r) = 0.9\log(1.2r + 1.05(1-r))+0.1\log(1.05(1-r))<br />
</math><br />
<br />
It is a simple calculus problem to show that G(r) is maximized by r = 0.2 with: <br />
G(0.2) = 0.05183. Then e^{0.05183} = 1.0532, showing that our maximum rate of growth is 5.32% as claimed by Peter. <br />
<br />
The attractiveness of the Kelly investment scheme is that, in the long run, any other investment strategy (including those where you are allowed to change your investment proportions at different times) will do less well. "In the long run and less well" means more precisely that the ratio of your return under the Kelly scheme and your return under any other strategy will tend to infinity.<br />
<br />
Thorp had a very good experience in the stock market, which is described very well by Gaeton Lion in his excellent [http://www.amazon.com/gp/product/customer-reviews/0809046377/ref=cm_cr_dp_pt/103-8647004-5865443?%5Fencoding=UTF8&n=283155&s=books review] of ''Fortune's Formula''. He writes:<br />
<br />
<blockquote> Ed Thorp succeeded in deriving superior returns in both gambling and investing. But, it was not so much because of Kelly's formula. He developed other tools to achieve superior returns. In gambling, Ed Thorp succeeded at Black Jack by developing the card counting method. He just used intuitively Kelly's formula to increase his bets whenever the odds were in his favor. Later, he ran a hedge fund for 20 years until the late 80s and earned a rate of return of 14% handily beating the market's 8% during the period. <br><br><br />
<br />
Also, his hedge fund hardly lost any value on black Monday in October 1987, when the market crashed by 22%. The volatility of his returns was far lower than the market. He did this by exploiting market inefficiencies using warrants, options, and convertible bonds. The Kelly formula was for him a risk management discipline and not a direct source of excess return. </blockquote><br />
<br />
Shannon also made a lot of money on the stock market, but did not use Kelly's formula. In his [http://www.amazon.com/gp/product/customer-reviews/0809046377/ref=cm_cr_dp_pt/103-8647004-5865443?%5Fencoding=UTF8&n=283155&s=books review] Gaeton Lion writes<br />
<br />
<blockquote>Claude Shannon amassed large wealth by recording one of the best investment records. His performance had little to do with Kelly's formula. Between 1966 and 1986, his record beat even Warren Buffet (28% to 27% respectively). Shannon strategy was similar to Buffet. Both their stock portfolios were concentrated, and held for the long term. Shannon achieved his record by holding mainly three stocks (Teledyne, Motorola, and HP). The difference between the two was that Shannon invested in technology because he understood it well, while Buffet did not. </blockquote><br />
<br />
Finally, Thorp provided the following comments for the book cover:<br />
<br />
<blockquote>From bookies to billionaires, you'll meet a motley cast of characters in this highly original, 'outside the box' look at gambling and investing. Read it for the stories alone, and you'll be surprised at how much else you can learn without even trying. --Edward O. Thorp, author of ''Beat the Dealer'' and ''Beat the Market''.</blockquote><br />
<br />
Submitted by Laurie Snell.<br />
<br />
<br />
==Which foods prevent cancer?==<br />
<br />
Which of these foods will stop cancer? (Not so fast)<br><br />
New York Times, 27 September 2005, Sect. F, p. 1<Br><br />
Gina Kolata<br />
<br />
Among other examples, the article includes a [http://www.nytimes.com/imagepages/2005/09/26/science/20050927_CANCER_GRAPHIC.html data graphic] on purported benefits of dietary fiber in preventing colorectal cancer. Early observational studies indicated an association, but subsequent randomized experiments found no effect. <br />
<br />
More to follow.<br />
<br />
<br />
==Slices of risk and the <em>broken heart</em> concept==<br />
[http://www.gloriamundi.org/picsresources/news20050912.pdf How a Formula Ignited Market That Burned Some Big Investors],<br />
Mark Whitehouse, The Wall Street Journal, September 12, 2005.<br><br />
<br />
This on-line article relates how a statistician, David Li,<br />
unknown outside a small coterie of finance theorists, helped change the world of investing. <br />
<br />
The article focuses on a event last May when General Motors Corp's debt<br />
was downgraded to junk status, causing turmoil in some financial markets.<br />
The article gives a nice summary of the underlying financial instruments known<br />
as credit derivatives -<br />
investment contracts structured so their value depends on the behavior of some other thing or event -<br />
with exotic names like <br />
[http://en.wikipedia.org/wiki/Collateralized_debt_obligations collateralized debt obligations] and [http://en.wikipedia.org/wiki/Credit_default_swap credit-default swaps].<br />
<br />
The critical step is to estimate the likelihood that many of the companies <br />
in a pool of companies would go bust at once. <br />
For instance, if the companies were all in closely related industries,<br />
such as auto-parts suppliers, they might fall like dominoes after a catastrophic event.<br />
Such a pool would have a 'high default correlation'.<br />
<br />
In 1997, nobody knew how to calculate default correlations with any precision. <br />
Mr. Li's solution drew inspiration from a concept in actuarial science known as the <br />
<em>broken heart</em> syndrome - people tend to die faster after the death of a beloved spouse. <br />
Some of his colleagues from academia were working on a way to predict this<br />
death correlation, something quite useful to companies that sell life insurance and joint annuities.<br />
He says:<br />
<blockquote><br />
Suddenly I thought that the problem I was trying to solve was exactly like the problem these<br />
guys were trying to solve,.<br />
Default is like the death of a company, so we should<br />
model this the same way we model human life."<br />
</blockquote><br />
<br />
This gave him the idea of using [http://en.wikipedia.org/wiki/Copula_%28statistics%29 copulas], <br />
mathematical functions the colleagues had begun applying to actuarial science. <br />
Copulas help predict the likelihood of various events<br />
occurring when those events depend to some extent on one another. <br />
Until the events last May of this year, one of the most popular copulas for bond pools <br />
was the Gaussian copula, named after <br />
[http://en.wikipedia.org/wiki/Carl_Friedrich_Gauss Carl Friedrich Gauss], a 19th-century German statistician. <br />
<br />
===Further reading===<br />
* The [http://www.gloriamundi.org/picsresources/news20050912.pdf on-line article] gives more details about what went wrong in the financial markets in May and the search for a more appropriate copula to capture better the <em>broken heart</em> syndrome between companies.<br />
* [http://en.wikipedia.org/wiki/Wikipedia Wikipedia] is a very worthwhile on-line resource for definitions of technical words, such as [http://en.wikipedia.org/wiki/Copula_%28statistics%29 copula].<br />
<br />
Submitted by John Gavin.<br />
<br />
<br />
==Learning to speak via statistics and graph theory==<br />
<br />
[http://education.guardian.co.uk/tefl/teaching/story/0,15085,1576100,00.html Computer learns grammar by crunching sentences], Max de Lotbinière September 23, 2005, [http://www.guardianweekly.co.uk/ Guardian Weekly].<br><br />
[http://www.cornellsun.com/vnews/display.v/ART/2005/09/09/432118a84f6af Profs’ New Software ‘Learns’ Languages], Ben Birnbaum, 9 Sep 2005, Cornell Daily Sun.<br />
<br />
A language-learning robot may sound like science fiction but new software, developed by Cornell University psychology professor Shimon Edelman, with colleagues Zach Solan, David Horn and Eytan Ruppin from Tel Aviv University in Israel, is well on the way to constructing a computer program that can teach itself languages and make up its own sentences, the developers' claim.<br />
<br />
Unlike previous attempts at developing computer algorithms for language learning - "Automatic Distillation of Structure," or "ADIOS" for short - discovers complex patterns in raw text by repeatedly aligning sentences and looking for overlapping parts.<br />
Once it has derived a language's rules of grammar,<br />
it can then produce sentences of its own, simply from blocks of text in that language.<br />
<br />
It has been evaluated on artificial context-free grammars with thousands of rules, <br />
on natural languages as diverse as English and Chinese, <br />
on coding regions in DNA sequences and on protein data correlating sequence with function. <br />
<br />
Edelman comments:<br />
<blockquote><br />
Adios relies on a statistical method for pattern extraction and on structured generalisations <br />
- the two processes that have been implicated in language acquisition.<br />
Our experiments show that Adios can acquire intricate structures <br />
from raw data including transcripts of parents' speech directed at two- or three-year-olds.<br />
This may eventually help researchers understand how children, <br />
who learn language in a similar item-by-item fashion, and with little supervision, <br />
eventually master the full complexity of their native tongue.<br />
</blockquote><br />
<br />
[http://plus.maths.org/latestnews/may-aug05/adios/ Plus Magazine's website]<br />
offers a more logical explanation:<br />
<blockquote><br />
The ADIOS algorithm is based on statistical and algebraic methods performed on one of the most basic and versatile objects of mathematics - the graph.<br />
Given a text, the program loads it as a graph by representing each word by a node, or vertex, and each sentence by a sequence of nodes connected by lines. A string of words in the text is now represented by a path in the graph. <br><br />
<br />
Next it performs a statistical analysis to see which paths, or strings of words, occur unusually often. <br />
It then decides that those that appear most frequently - called "significant patterns" - <br />
can safely be regarded as a single unit<br />
and replaces the set of vertices in each of these patterns by a single vertex, <br />
thus creating a new, generalised, graph.<br><br />
<br />
Finally, the program looks for paths in the graph which just differ by one vertex. <br />
These stand for parts of sentences that just differ by one word (or compound of words) like "the cat is hungry" and "the dog is hungry". <br />
Performing another statistical test on the frequency of these paths, the program identifies classes of vertices, or words, that can be regarded as interchangeable, or equivalent. <br />
The sentence involved is legitimate no matter which of the words in the class - in our example "cat" or "dog" - you put in.<br><br />
<br />
This last step is then repeated recursively.<br><br />
</blockquote><br />
<br />
[http://plus.maths.org/latestnews/may-aug05/adios/ The website] uses graphs to illustrate some examples and it finishes with some reassuring words:<br />
<blockquote><br />
All this doesn't mean, of course, that the program actually "understands" what it's saying. It simply knows how to have a good go at piecing together fragments of sentences it has identified, in the hope that they are grammatically correct. So if, like me, you're prone to swearing at your computer, you can safely continue to do so: it won't answer back for a long while yet.<br />
</blockquote><br />
<br />
===Further reading===<br />
The [http://adios.tau.ac.il/ ADIOS homepage] offers an overview and more detailed description of the program.<br />
<br />
Submitted by John Gavin.<br />
<br />
==Understanding probability==<br />
<br />
Understanding Probability:Chance rules in everyday life<br><br />
Cambridge University Press 2004<br><br />
Henk Tijms<br />
<br />
Hank Tijms is Professor in Operation Research at the Vrije University in Amsterdam. This book is based on his earlier Dutch book “Spelen met Kansen.” <br />
<br />
The aim of this book is to show how probability applies to our everyday life in a way that your Uncle George could understand even if he has forgotten much of his high school math. Tijms does not try to avoid mathematics but only to postpone the formal math until the reader has seen the many applications of probability in the real world, how much fun it is, and learned to work problems and when he can’t work one how to get the answer by simulation. He learns all this in part I of the book and then he learns the more formal math in Part II.<br />
<br />
In Chapter 1 Tijms asks the reader to think about problems with surprising answers in the spirit of Susan Holmes “[http://www-stat.stanford.edu/~susan/surprise/ Probability by Surprise]” including the birthday problem and the Monty Hall problem. Readers are on their own to try to solve one or more of the problems but promised that they will see the solutions later in the book. <br />
<br />
Chapter 2 deals with the law of large numbers and introduces the concept of simulation. This theorem is explained and illustrated by problems related, for example, to coin tossing, random walks and casino games. Expected value is introduced in an informal way to be defined more carefully later in the book. For the reader who is not frightened by mathematical formulas, Tijms includes a discussion of the Kelly betting system with a footnote saying that this paragraph can be skipped at first reading. This is a fascinating topic that is widely applied in gambling and stock investment but rarely appears in a probability book.<br />
<br />
In Chapter 3 the author returns to previous problems such as the birthday problem and gambling systems and solves them first by simulation and then by mathematics. <br />
<br />
In this chapter Tijms describes Efron’s bootstrap method and uses it to solve a number of problems including a hypothetical clinical trial and to test if the famous 1970 draft lottery during the Vietnam War was fair. Again the bootstrap method has wide application but rarely occurs in an elementary probability or statistics book.<br />
<br />
Chapter 4 describes the binomial, Poisson, and hypergeomtric distributions and how to use them in solving problems such as the famous hat check problem, and a variety of interesting lottery questions. The Poisson process is discussed but again with the footnote that novice readers might want to read this at a later time.<br />
<br />
Chapter 5 is mainly about Center Limit Theorem and its many applications especially to statistics. <br />
<br />
Chapter 6 introduces Chance trees and Bayes’s rule. The tree method is used to explain a variety of problems including the Monty Hall Problem and the false-positive paradox. <br />
<br />
This is a brief description of the first six chapters which constitute Part I of the book. Now the fun is over. Part 2 called “Essentials of probability” looks like the traditional first chapters in a standard probability book. But the reader has already found how exciting probability is, has a good intuitive idea of the basic concepts and has worked many of the interesting problems at the end of each chapter either using math or simulation. For some students this might allow them to actually enjoy Part 2. But your Uncle George may want to quit while they are ahead. <br />
<br />
Tijms writes with great clarity and his enthusiasm for probability in the real world is contagious. We were delighted to see, as acknowledged in the preface, that Tijms included several of the more interesting problems discussed in Chance News, often going well beyond what we had said in our discussion of the problem. <br />
<br />
This book presents a completely new way to go about teaching a first course in probability and we think those who teach such a course should consider trying it out.<br />
<br />
===Discussion===<br />
<br />
(1) In the days of Basic we required all students to learn Basic in their first math course so we could assume that students could write programs to simulate probability problems and so me made heavy use of simulation as suggested in this book. The author uses Pascal in his book. What present language do you think is easiest for a student with no computing experience to learn?<br />
<br />
We asked Professor Tijms what the situation was in math departments in Europe and he replied:<br />
<br />
<blockquote>In math departments of universities and polytechnic schools in Europe students learn to write computer programs. In my university they still learn to program in Java and C++ ( in previous days Pascal), but I see in the Netherlands the trend that the instructors think it is sufficient if the students are able to program in Matlab. <br><br><br />
<br />
In ny book I have chosen to formulate the simulation programs in Pascal because of the clarity and the simplicity of the language, though this language is hardly used anymore. The introductory probability course at my university is given before they have learned to program, but this does not prevent them of simulating probability problems by using Excel. In the simulation of many elementary probability problems a random-number generator alone suffices to simulate those problems and so Excel can be used. In the second year they have mastered Matlab, a perfect tool with its excellent graphics to simulate many challenging probability problems ( they really like it, in particular when it concerns problems such as the problems 2.24-2.45 in chapter 2 and the problems 5.11-5.13 in chapter 5). <br />
</blockquote><br />
<br />
<br />
(2) Do you think that probability books should include data to test probability models that are said to describe real world problems? If so name some models that you think would pass such a test and some that you think might not.<br />
<br />
Submitted by Laurie Snell<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Societies worse off when they have God on their side==<br />
<br />
[http://www.timesonline.co.uk/article/0,,2-1798944,00.html Societies worse off when they have God on their side]<br><br />
Timesonline, September 27, 2005<br><br />
Ruth Gledhill<br />
<br />
[http://moses.creighton.edu/JRS/2005/2005-11.html Cross-national correlations of quantifiable societal health with popular religiosity and secularism in the prosperous democracies]<br><br />
Journal of Religion & Society, Vol.7(2005)<br><br />
Gregory S. Paul<br />
<br />
In the Times article we read:<br />
<br />
<blockquote>According to the study, belief in and worship of God are not only unnecessary for a healthy society but may actually contribute to social problems.<br><br><br />
Many liberal Christians and believers of other faiths hold that religious belief is socially beneficial, believing that it helps to lower rates of violent crime, murder, suicide, sexual promiscuity and abortion. The benefits of religious belief to a society have been described as its “spiritual capital”. But the study claims that the devotion of many in the US may actually contribute to its ills. <br />
</blockquote><br />
<br />
Gregory Paul is a dinosaur paleontologist and on an [http://www.abc.net.au/worldtoday/indexes/2005/twt_20050928.htm interview] on Australian ABC radio Paul said that, being a paleontologist, for many years he had to deal with the issue of creationism versus evolutionary science in the U.S and his interest in evolutionary science prompted him to look at whether there was any link between the religiosity of a society and how well that society functions. <br />
<br />
If you look at Paul's article you will find very little technical statistical analysis, for example, he did not carry out a regression analysis. Rather he rests his case on the series of scatterplots.<br />
<br />
Paul describes his data sources as:<br />
<br />
<blockquote>Data sources for rates of religious belief and practice as well as acceptance of evolution are the 1993 Environment I (Bishop) and 1998 Religion II polls conducted by the International Social Survey Program (ISSP), a cross-national collaboration on social science surveys using standard methodologies that currently involves 38 nations. The last survey interviewed approximately 23,000 people in almost all (17) of the developed democracies; Portugal is also plotted as an example of a second world European democracy. Results for western and eastern Germany are combined following the regions' populations. England is generally Great Britain excluding Northern Ireland; Holland is all of the Netherlands. The results largely agree with national surveys on the same subjects; for example, both ISSP and Gallup indicate that absolute plus less certain believers in a higher power are about 90% of the U.S. population. The plots include Bible literalism and frequency of prayer and service attendance, as well as absolute belief in a creator, in order to examine religiosity in terms of ardency, conservatism, and activities. </blockquote><br />
<br />
Here are the countries Paul considered with the abbreviations used on the graphics. <br />
<br />
A = Australia, C = Canada, D = Denmark, E = Great Britain, F = France, G = Germany,<br />
H = Holland, I = Ireland, J = Japan, L = Switzerland, N = Norway, P = Portugal, R = Austria,<br />
S = Spain, T = Italy, U = United States, W = Sweden, Z = New Zealand.<br />
<br />
There seems to be no agreement as to which countries are developed democracies. For example Paul might have included Greece and Belgium, Finland, and others but the data may have determined his choice. Paul comments that he added Portugal as an example of a second world democracy. <br />
<br />
Paul's anaysis of the data includes a series of 9 Figures which are available at the end of the article and are the most interesting part of the study. If you try printing Paul's article you will only get the first of his 9 Figures. When you look at the [http://moses.creighton.edu/JRS/2005/2005-11.html web version] you will still see only Figure 1 but the others can be viewed by selecting the numbers from 2 to 9 on the left side of Figure 1.<br />
<br />
Figure 1 deals with the proportion of people who accept human evolution which is interesting but not as relevant to the welfare of the people as others so we will look at Figure 2.<br />
<br />
[[Image:religion2.png|500px|center|Source:Gregory Paul]]<br />
<br />
Each Figure iprovides 5 separate scatterplots. Ïn Figure 2 we see that the U.S. has largest number--between 6 and 7-- of homicides per 100,000 and Spain has the lowest number with less than 1 homicide per 100,000. We also see that the U.S. has the highest proportion of people, about 25%, who take the bible literally while several countries have less than 10% such people.<br />
<br />
What we cannot do is compare the number of homicides per thousand between those who take the bible literally and those who are agnostics or atheists which is what we would really want to know. Presumably the data did not permit this comparison. <br />
<br />
[[Image:religion3.png|500px|center|Source:Gregory Paul]]<br />
<br />
Figure 3 deals with "14-24 year old suicides per 100,000". Here the U.S. is in about the middle.<br />
<br />
Figure 4 deals with the "under-five mortalities per 1000 births".<br />
<br />
[[Image:religion4.png|500px|center|Source:Gregory Paul]]<br />
<br />
Ignoring Portugal, the U.S. has the highest number of under-five mortalities per 1000 births-- between 7 and--8 while several countries have only 4.<br />
<br />
The other figures can be seen at end of Paul's article. They deal with life expectancy, sexually transmitted diseases, abortion and 15-16 year old pregnancies. Life expectancy is the smallest in the U.S. and for sexually transmitted diseases, abortion and 15-17 year old prenacies the U.S. is at the top of the graphs and in fact these look like outliers.<br />
<br />
Well, this study does not by itself justify the Times hedline: "Societies worse off when they have God on their side." Paul himself would not claim this. He writes:<br />
<br />
<blockquote> This study is a first, brief look at an important subject that has been almost entirely neglected by social scientists. The primary intent is to present basic correlations of the elemental data. Some conclusions that can be gleaned from the plots are outlined. This is not an attempt to present a definitive study that establishes cause versus effect between religiosity, secularism and societal health. It is hoped that these original correlations and results will spark future research and debate on the issue.</block<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div></div>Nano12https://www.causeweb.org/wiki/chance/index.php?title=Chance_News_8&diff=1543Chance News 82005-11-05T09:33:54Z<p>Nano12: /* Quotation */</p>
<hr />
<div>Oct 15 to Oct 30<br />
<br />
==Quotation==<br />
<blockquote>One more fagot of these adamantine bandages, is, the new science of Statistics. It is a rule, that the most casual and extraordinary events -- if the basis of population is broad enough -- become matter of fixed calculation. It would not be safe to say when a captain like Bonaparte, a singer like Jenny Lind, or a navigator like Bowditch, would be born in Boston: but, on a population of twenty or two hundred millions, something like accuracy may be had. Ralph Waldo Emerson Fate</blockquote><br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Forsooth==<br />
Here's another Forsooth from the October issue of RSS News.<br />
<blockquote>Your'e more likely to die in a fire in Strathclyde than anywhere else in the country</blockquote><br />
<br />
<div align="right">BBC1 mews bullietin<br><br />
11 May 2005</div><br />
<br />
==The Poisson distribution and the Supreme Court==<br />
The Poisson distribution and the Supreme Court<br><br />
''Journal of the American Statistical Association'' 31, no. 195 ,(1936), 376-80<br><br />
W. Allen Wallis<br />
<br />
Supreme Court Appointments as a Poisson distribution<br><br />
''American Journal of Political Science'', 26, No.1, February 1982<br><br />
S. Sidney Ulmer<br />
<br />
This is not current news, but since Supreme Court appointments are in the news we felt that these articles might make an interesting class discussion.<br />
<br />
In 1936 statistician Allen Wallis suggested that a Poisson distribution can approximate the number of U.S. Supreme Court appointments in a given year. In his Table 1 Wallis provided the number appointed in each year over the intervals with different numbers of Justices on the Supreme Court: 1790-1806 (6) 1807-1836 (7), and 1837-1932 (9). Actually there were 10 in the years 1963 to 1967 which Wallis called "negligible exceptions."<br />
<br />
[[Image:wallis1.png|500px|center]]<br />
<br />
Wallis then restricts himself to the years 1837-1932 and finds that a Poisson distribution with mean .5 can approximate the number of court appointments in a year. His results are shown in his Figure II:<br />
<br />
[[Image:wallis2.png|500px|center]]<br />
<br />
In his article, Sidney Ulmer updated the data to 1980 and also includes data from the early Supreme Courts with 6 and 7 members. Thus his data covers the years 1790--1980. His Table 1 compares the actual number of appointments in a year with the expected number of appointments assuming a Poisson distribution with mean 5.13.<br />
<br />
[[Image:ulmer1.png|500px|center]]<br />
<br />
In his Table II Ulmer limits the data to the 9 member Supreme Courts: 1837 to 1862 and 1869-1980).<br />
<br />
[[Image:ulmer2.png|500px|center]]<br />
<br />
Testing the goodness of fits, Ulmer argues that the fit with the varying size Supreme Courts is just as good as with fixed size Supreme Courts.<br />
<br />
===DISCUSSION===<br />
<br />
(1) What is the probability that a President will make 2 or more appointments to the Supreme Court during a 4-year term? What is the probability a President makes no appointments during a 4-year term? Has this ever happened?<br />
<br />
(2) Do you agree with Ulmer that there is no reason to limit the data to years with the Supreme Court is the same size?<br />
<br />
(3) Obtain the data needed to update Ulmer's results to today and provide Tables that correspond to Ulmer's Tables 1 and 2. Add your Tables to this Chance News and make your data available to make it easier to update this in future years.<br />
<br />
Contributed by Laurie Snell<br />
<br />
==Possible Cancer Cluster in Connecticut==<br />
Pratt Agrees to Increase Funding for Brain Cancer Study <br><br />
''The Associated Press''<br><br />
October 11, 2005<br><br />
Stephen Singer<br><br />
<br />
<br />
In a case that seems eerily familiar to the leukemia cancer cluster made famous by the book and movie, ''A Civil Action'', researchers are trying to determine whether or not a cancer cluster exists among workers at Pratt & Whitney, a company that manufactures jet engines. Over one hundred former or current Pratt & Whitney employees have been identified as having a relatively rare type of fatal brain tumor known as glioblastoma multiforme, which strikes 3 people per 100,000 every year. Many of these workers have been exposed to metals and chemical substances, including TCE (trichloroethylene), which is an engine degreaser. TCE is the same carcinogenic chemical that was dumped in the 1960’s and 1970’s by the chemical company, WR Grace, in Woburn, MA, and that was found to have contaminated the drinking water in two of the town’s wells. <br><br />
<br />
<br />
Prior to the recent announcement that the funding is being increased from $6 million dollars to $12 million dollars, this medical study was already being described as the largest occupational health study ever conducted. It covers 250,000 people who worked at any of the seven Connecticut Pratt & Whitney plants from 1952 to 2001. So far, at least 125 cases of brain cancer have been documented, according to the lawyer who represents dozens of individuals and family members.<br><br />
<br />
<br />
The study falls under the auspices of the Connecticut Department of Public Health. However, due to the overwhelming cost and scope of the study, Pratt & Whitney is funding the project. Since Pratt is paying for the study, they chose the researchers, a team from the University of Pittsburgh. The project began three years ago, and the results are expected to be available between 2007 and 2009.<br><br />
<br />
<br />
In the meantime, this case faces many of the obstacles common in the quest to establish whether or not a cancer cluster exists, such as proving causation, the fact that it can take a long time (sometimes 5-40 years) after exposure for true problems to show up, and finding the people who were exposed & convincing them to participate in the study. Additionally, there are legal difficulties for the families involved, including Connecticut’s statute of limitations laws, the length of time it takes investigators to reach a conclusion, the cost of litigation, and the “deep pockets” of a company like Pratt & Whitney.<br><br />
<br />
<br />
This case study provides a current example of an ongoing investigation into a possible cancer cluster. Will it ultimately be found to be a coincidence cluster or proven to be a true cancer cluster? Does it make sense that the researchers are including in the study everyone who worked at Pratt over a fifty year period, even those who only worked there for a brief time period and those who were not directly exposed to toxic substances (i.e. office workers)? Could the researchers possibly have an unconscious bias in favor of the company that is funding their research? If the company doesn’t fund the research, then who should? Is there some other way to structure such investigations, so that the company involved pays for the study, but is not allowed to choose the researchers and directly fund them?<br><br />
<br />
<br />
'''Further Reading'''<br><br />
<br />
• “Rare Cancer Found in Workers”, ''The New York Times'', March 10, 2002, Jane Gordon<br><br />
• “Scientist: Pratt Commits to Cancer Study”, ''The Hartford Courant'', May 19, 2005<br><br />
• “Participation in Cancer Study at Pratt Lagging”, ''The Hartford Courant'', October 12, 2005, Paul Marks<br><br />
• ''The New Haven Advocate'' has had more than a dozen articles that explain the working conditions at Pratt & Whitney, and also chronicle the history & progression of this case. These articles have been investigated and written primarily by Carole Bass, Associate Editor. A few of the articles are listed below. <br> <br />
-“Worked to Death”, August 2, 2001, Carole Bass & Camille Jackson<br><br />
-“Talking Cure”, October 28, 2004, Dave Goldberg<br><br />
-“Time’s Not on Their Side”, January 20, 2005, Carole Bass<br><br />
-“The Brains Behind the Brain”, October 20, 2005, Carole Bass <br><br />
For the early New Haven Advocate articles (i.e., 2001-2002) on this subject, go to http://old.newhavenadvocate.com/workedtodeath/index.html<br> <br />
For the articles since 2002, go to <br><br />
http://www.newhavenadvocate.com and search for Pratt & Whitney.<br><br />
<br />
Submitted by Josephine Rodriguez.<br />
<br />
==A record powerball lottery jackpot==<br />
<br />
On Saturday Oct 22, 2005 the powerball lottery had a record powerball jackpot of 340 million dollars. <br />
<br />
When you buy a ticket for this lottery, you specify five distinct numbers from 1 to 55, which we call basic numbers and one number from 1 to 42 called the bonus number. To win the Jackpot your 5 basic numbers and your bonus number must agree with a random choice of 5 basic numbers and one bonus number chosen by the lottery officials. The number of possible tickets is:<br />
<br />
<center><math>{55 \choose 5} 42 = </math> 146,107,962</center><br />
<br />
Thus if you buy a single ticket, the probability of having a winning jackpot ticket is<br />
<br />
<center> <math>{1} \over {146107962}</math> = .000000006844...</center><br />
<br />
The powerball website and the media expresses this by saying that the odds that you have a winning jackpot ticket is 1 in 146,107,962. <br />
<br />
Whenever there is a record jackpot, the news writers look for suggestions for other rare events that might be more familiar to its readers. <br />
<br />
Our own favorite was suggested by Fred Hoppe: if you toss a coin 27 times your chance of getting 27 heads in a row is greater than your chance of having a winning jackpot ticket when you buy a single ticket. (<math> 2^{27} = 134217728</math> and so there are 134,217,728 possible sequences of heads and tails and only 1 has all heads.)<br />
<br />
In an article for the ''Omaha World-Herald'' Oct 18, 2005 , Robynn Tysver writes:<br />
<br />
<blockquote> You have a greater chance of getting killed by lightning than winning this week's 340 million Powerball jackpot. You also have a greater chance of drowning in a bathtub. The lifetime odds of getting killed by lightning are one in 56,439, and the lifetime odds of dying while in or falling into a bathtub are one in 10,582, according to the National Safety Council. <br />
</blockquote><br />
<br />
These are not even in the ballpark. The ''Minneapolis Star Tribune'' consulted mathematicians David Bressoud and Douglas Arnold who contributed the following:<br />
<br />
According to Arnold you have a seven times better chance of becoming a saint. And Bressoud notes that you're six times more likely to get elected president of the United States. But they also provide the following more interesting estimates:<br />
<br />
<blockquote>Bressoud: "If you buy 10 tickets a week, every week, it would take you 280,000 years before you could expect to win."<br><br><br />
<br />
Arnold: "If you were to select a group of Powerball numbers every minute for 138 years, you would have about a 50 percent chance of picking the winning Powerball ticket." <br><br><br />
<br />
It is not clear what Bressoud means by "expect to win". We can check this by a simple calculation (simple for Mathematica). Let q(n) be the probability that you if you buy n tickets you fail to get a winning jackpot ticket . Then:<br />
<br />
<center> <math> \left(\frac{146107961}{146107962}\right) ^n = q(n) </math></center><br />
<br />
The average number of weeks in a year is 52.177457 so If you buy 10 tickets a week, every week for 280,000 years you will buy about 146,097,000 tickets. Using this number for n in our formula we find that you have about a 37% chance of not getting a winning lottery ticket or a 63% chance of getting one. We would not "expect to win" with a 63% chance of winning but others may. Using our formula for q(n) we find that if we buy 10 tickets a week, every week for 830,000 years you will have about a 95% chance of getting at least one winning lottery ticket which seems to us more appropriate for expecting to win. <br />
<br />
Consider now Arnold's example. Our colleague Dana Williams found that you need to buy a ticket for about 101 million lottery offerings to have about a 50% chance of getting at least one winning lottery ticket. There are an average of 525,946.766 minutes in a year. Dividing 101 million by this number gives 192.035. Thus Arnold's 138 years should be 192 years.<br />
<br />
We asked Professor Arnold about this and he replied:<br />
<br />
<blockquote> That number, which was quoted in the ''Star Tribune'' was an off-the-top-of-my-head calculation made when the reporter called me on<br />
the phone with no warning. Right ballpark, but not very accurate. Later I redid the calculation carefully.</blockquote><br />
<br />
Arnold's computations were similar to ours but he used a greater accuracy for the number of independent lotteries you have to buy to have a 50% chance of choosing the jackpot numbers at least once. His answer to this was 101,274,322. Using this, Arnold's estimate for the number of years, buying a ticket every minute, to have a 50% chance of winning a jackpot is193 years instead of our estimate of 192 years.<br />
<br />
Arnold said that he also estimated the expected value of a $1 ticket. To do this he needed an estimate for the number of tickets sold. He was told that a reasonable estimate was 106 million. In calculating the expected value of a $1 ticket he used the cash value of 164.4 million dollars instead of the annuity payout of 340 million dollars. He also took into account the possibility of having to share the jackpot. Doing this he got an expected value of exactly $1, just the price of the ticket. He commented that if he took into account the taxes the expected value would be more like 80 cents making even this lottery an unfavorable event.<br />
<br />
The news writers also gave a lot of coverage of Senator Gregg (Chairman of the Senate Budget Committee) winning $853,492 for getting the second highest prize: getting the 5 basic numbers correct but note the bonus number. Normally the prize for getting this is $200,000 cash but Gregg was the beneficiary of recent change in the powerball lottery. <br />
<br />
The powerball officials have found that increasing the size of the jackpot can increase the ticket sales because of the public's interest in large jackpots. They do this by increasing the number of possible basic numbers. When they started in 1992, to get the jackpot you had to get the 5 basic numbers chosen from 45 numbers and the 1 bonus number chosen from 45 number correct. Here are the changes so far<br />
<br />
<center><br />
1992 5 of 45 1 of 45<br><br />
1997 5 or 49 1 of 42<br><br />
2002 5 of 55 1 of 42<br><br />
2005 5 of 55 1 of 42<br><br />
</center><br />
<br />
While the lottery officials want to have higher jackpots, they also do not want too long a period between jackpots. Normally the increase in the size of the lottery, when no one wins the jackpot, is determined by the amount taken in in this unsuccessful drawing. This was recently changed so that, when a new record jackpot occurs and no-one wins it, at most 25 million dollars are added to the Jackot until someone wins the jackpot. The money save by this is added to the second prize.<br />
<br />
When the 340 million jackpot was won, 49 players had the five basic numbers correct but not the bonus numbers. For these winners the $200,000 prize had 653,492 added to their prize so they each won $853,492. If they chosen the Powerball play option for an extra $1 their $200,000 would have been multiplied by 2,3,4, or 5 with equal probabilities. Thus if Gregg had chosen the Powerball play option, and been lucky, he would have won 1,653,492 dollars that he could add to his 15 or so million dollars he has in stocks. <br />
<br />
===DISCUSSION===<br />
<br />
(1) Do you think it is fair to advertise the lottery prize as 340 million when the cash prize is only 164.4 million?<br />
<br />
(2) What is the probability of winning the second prize?<br />
<br />
(3) Assuming that the estimate 106 million for the number of tickets sold find the expected number of second prize winners.<br />
<br />
==Mammograms Validated as Key in Cancer Fight==<br />
<br />
The ''New York Times'' [http://www.nytimes.com/2005/10/27/health/27breast.html reported] on October 27, 2005 on a new National Cancer Institute study that attributed a significant decrease in the death rate from breast cancer to mammogram screening tests. The study, published in the New England Journal of Medicine, found that from 28% to 65% of the sharp 24% decrease in breast cancer death rates from 1990 to 2000 was due to screening; the remainder was attributed to new drugs used to treat the disease.<br />
<br />
Prior to this study, the value of mammogram screening had been disputed, for several reasons. In the general population, the test results in a large proportion number of false positives, about 90%. Thus, many women who are cancer-free are subjected to unnecessary procedures. Also, approximately 30% of cancers that are detected and treated would not have progressed significantly. Unfortunately, it isn't possible to distinguish between these so-called ''indolent'' cancers and those that become life-threatening, so it is routine practice to treat them all.<br />
<br />
The new study suggests that the benefits of routine mammography are more certain than earlier believed, according to Don Berry, Chairman of the biostatistics department of M. D. Anderson Cancer Center, in Houston, Texas, and the lead author of the paper. He said that the new study for the first time properly separates the effects of therapy and screening. Nonetheless, he cautioned that mammography does pose risks, and recommended that women be counselled before screening.<br />
<br />
Contributed by Bill Jefferys<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div></div>Nano12https://www.causeweb.org/wiki/chance/index.php?title=Chance_News_7&diff=1542Chance News 72005-11-05T09:33:50Z<p>Nano12: /* Quotation */</p>
<hr />
<div>Sept 26 2005 to Oct 15 2005<br />
==Quotation==<br />
<blockquote><br />
While writing my book [Stochastic Processes] I had an argument with Feller [Introuction to Probability Theory and its Applications]. He asserted that everyone said "random variable" and I asserted that everyone said "chance variable." We obviously had to use the same name in our books, so we decided the issue by a stochastic procedure. That is, we tossed for it and he won. </blockquote><br />
<br />
<p align = right> Joe Doob<br><br />
[http://www.dartmouth.edu/~chance/Doob/conversation.html Statistical Science]<br><br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Forsooth==<br />
<br />
Peter Winkler suggested our first forsooth.<br />
<br />
<blockquote>Texas beats Ohio State in their opening game <br />
of the season (Saturday Sept 10 2002). The sportscasters (legendary Brent Musburger on play-by-play or Gary Danielson on analysis) observed that of the 14 teams who have <br />
previously played in the championship game (at the end of each season) 5 <br />
have suffered an earlier defeat. "Thus," they conclude, "Ohio State can <br />
still make it to the championship game, but their chances are now less <br />
than 50%."</blockquote><br />
<br />
===Discussion===<br />
<br />
What is wrong with this?<br />
----<br />
Here are forsooths from the September 2005 issues of RSS NEWS<br />
<br />
<blockquote>'Big ticket quiz' at the start of Wimbledon:<br><br><br />
Q. How many punnets (a small light basket or other container for fruit or vegetables) of strawberries are eaten each day during the Wimbledon tournament?<br><br />
Is it (a) over 8,000, (b) over 9,000 or (c) over 10,000?</blockquote><br />
<br />
<div align="right">BBC radio 5<br><br />
20 June 2005</div><br />
<br />
<blockquote>Waiting time for foot surgery down by 500%</blockquote><br />
<br />
<div align="right">Evening News (Edinburgh)<br><br />
5 July 2005</div><br />
<br />
The next two forsooths are from the October RSS news.<br />
<br />
<blockquote>In 1996-8 when the number attending university was static, the participation of women was also static, but male participation fell.</blockquote><br />
<br />
<div align="right">The Times Higher<br><br />
21 January 2005</div><br />
<br />
<blockquote>[On the subject of congestion on the London Underground..] 'Last year 976 million of us used the tube...'</blockquote><br />
<br />
<div align="right">BBC London News<br><br />
19 May 2005</div><br />
<br />
<br />
==Fortune's Formula==<br />
<br />
''Fortune's Formula: Wanna Bet?''<br><br />
''New York Times Book Section'', September 25, 2005<br><br />
David Pogue<br />
<br />
This must be the kind of review that every Science writer dreams of. Pogue ends his review with:<br />
<br />
<blockquote> ''Fortune's Formula'' may be the world's first history book, gambling primer, mathematics text, economics manual, personal finance guide and joke book in a single volume. Poundstone comes across like the best college professor you ever had, someone who can turn almost any technical topic into an entertaining and zesty lecture. But every now and then, you can't help wishing there were some teaching assistants on hand to help.</blockquote><br />
<br />
The author William Poundstone is a science writer who has written a number of very successful science books. His book, ''Prisoner's dilemma: John von Neumann, game theory and the puzzle of the bomb'', was written in the style of this book. Indeed Helen Joyce, in her review of this book in Plus Magazine writes:<br />
<br />
<blockquote>This book is a curious mixture of biography, history and mathematics, all neatly packaged into an entertaining and enlightening read. </blockquote><br />
<br />
Poundstone describes himself as a visual artist who does books as a "day job.". You can learn about his art work [http://www.uiowa.edu/~iareview/tirweb/feature/poundstone/interview2.htm here].<br />
<br />
''Fortune's Formula'' is primarily the story of Edward Thorp, Claude Shannon, and John Kelly and their attempt to use mathematics to make money gambling in casinos and on the stock market. None of these did their graduate work in mathematics. Thorp and Kelly got their Phd's in physics and Shannon in Genetics. <br />
<br />
In the spring of 1955, while a graduate student at UCLA, Thorp joined a discussion on the possiblity of making money from roulette. Thorp suggested that they could taking advantage of the fact that bets are still accepted for a few second after the croupier releases the ball, and in these seconds, he could estimate what part of the wheel the ball would stop. <br />
<br />
Thorp did not pursue this and in 1959 became an instructor in mathematics at M.I.T. Here he became interested in blackjack and developed his famous card counting method for wining at blackjack. He decided to publish his method in the most prestigious journal he could find and settled on ''Proceedings of the National Academy of Sciences''. For this he needed to have a member of the Academy submit his paper. The only member in the math department was Shannon so he had to persuade him of the importance of his paper. Shannon not only agreed but in the process became fascinated by Thorp's idea for beating roulette. He agreed to help Thorp carry this out. They built a roulette machine in Shannon's basement. It worked fine there in trial runs but not so well in the casino so they did not pursue this method of getting rich. <br />
<br />
Of course Thorp is best known for showing that blackjack is a favorable game and giving a method to exploit this fact. Shannon is best known for his work in information theory. Kelly is known his method for gambling in a favorable game. This plays a central role in Poundstone's book and is probably why Pogue felt that it would help if he had a teaching assistant. Poundstone tries to explain Kelly's work in many different ways but what he really needed to understand it is an example but this required too many formulas for a popular book. So we shall include an example from Chance News 7.09. <br />
<br />
Writing for Motley Fool, 3 April 1997 Mark Brady complained about the inumeracy of the general public and gave a number of examples including this one:<br />
<br />
<blockquote> Fear of uncertainty and innumeracy are synergistic. Most people cannot do the odds. What is a better deal over a year? A 100% safe return with 5 percent interest or a 90 percent safe return with a 20 percent return. For the first deal, your return will be 5% percent. For the second, your return will be 8%. Say you invest $1000 10 times. Your interest for the 9 successful deals will be 9000 x 0.2 or 1800. Subtract the 1000 you lost on the 10th deal and you get a $800 return on your original $10,000 for 8 percent.</blockquote><br />
<br />
Peter Doyle suggested that a better investment strategy in this case is:<br />
<br />
Faced with a 100 percent-safe investment returning 5 percent and a 90 percent-safe investment returning 20%, you should invest 20% of your funds in the risky investment and 80% in the safe investment. This gives you an effective return of roughly 5.31962607969968292 percent. <br />
<br />
Peter is using a money management system due to J. L. Kelly (1956: "A new interpretation of information rate," ''Bell System Technical Journal'', '''35'''). Kelly was interested in finding a rational way to invest your money faced with one or more investment schemes, each of which has a positive expected gain. He did not think it reasonable to try simply to maximize your expected return. If you did this in the Motley Fools example as suggested by Mark Brady, you would choose the risky investment and might well lose all your money the first year. We will illustrate what Kelly did propose in terms of Motley Fools example. <br />
<br />
We start with an initial capital, which we choose for convenience to be $1, and invest a fraction r of this money in the gamble and a fraction 1-r in the sure-thing. Then for the next year we use the same fractions to invest the money that resulted from the first year's investments and continue, using the same r each year. Assume, for example, that in the first and third years we win the gamble and in the second year we lose it. Then after 3 years our investment returns an amount f(r) where: <br />
<br />
<math><br />
f(r) = (1.2r + 1.05(1-r))(1.05(1-r))(1.2r + 1.05(1-r)). <br />
</math><br />
<br />
After n years, we would have n such factors, each corresponding to a win or a loss of our risky investment. Since the order of the terms does not matter our capital will be: <br />
<br />
<math><br />
f(r,n) = (1.2r + 1.05(1-r))^W(1.05(1-r))^L<br />
</math><br />
<br />
where W is the number of times we won the risky investment and L the number of times we lost it. Now Kelly calls the quantity:<br />
<br />
<math><br />
G(r) =\lim_{n \to \infty }\frac{\log(f( r,n)} {n}<br />
</math> <br />
<br />
the exponential rate of growth of our capital. In terms of G(r) our capital should grow like <math> e^{G(r)} </math>. In our example: <br />
<br />
<math><br />
\log(\frac{f(r,n)}{n}) = \frac{W}{n}\log(1.2r + 1.05(1-r)) + \frac{L}{n}\log(1.05(1-r))<br />
</math> <br />
<br />
Since we have a 90% chance of winning our gamble, the [http://en.wikipedia.org/wiki/Strong_law_of_large_numbers#The_strong_law strong law of large numbers] tells us that as n tends to infinity this will converge to <br />
<br />
<math><br />
G(r) = 0.9\log(1.2r + 1.05(1-r))+0.1\log(1.05(1-r))<br />
</math><br />
<br />
It is a simple calculus problem to show that G(r) is maximized by r = 0.2 with: <br />
G(0.2) = 0.05183. Then e^{0.05183} = 1.0532, showing that our maximum rate of growth is 5.32% as claimed by Peter. <br />
<br />
The attractiveness of the Kelly investment scheme is that, in the long run, any other investment strategy (including those where you are allowed to change your investment proportions at different times) will do less well. "In the long run and less well" means more precisely that the ratio of your return under the Kelly scheme and your return under any other strategy will tend to infinity.<br />
<br />
Thorp had a very good experience in the stock market, which is described very well by Gaeton Lion in his excellent [http://www.amazon.com/gp/product/customer-reviews/0809046377/ref=cm_cr_dp_pt/103-8647004-5865443?%5Fencoding=UTF8&n=283155&s=books review] of ''Fortune's Formula''. He writes:<br />
<br />
<blockquote> Ed Thorp succeeded in deriving superior returns in both gambling and investing. But, it was not so much because of Kelly's formula. He developed other tools to achieve superior returns. In gambling, Ed Thorp succeeded at Black Jack by developing the card counting method. He just used intuitively Kelly's formula to increase his bets whenever the odds were in his favor. Later, he ran a hedge fund for 20 years until the late 80s and earned a rate of return of 14% handily beating the market's 8% during the period. <br><br><br />
<br />
Also, his hedge fund hardly lost any value on black Monday in October 1987, when the market crashed by 22%. The volatility of his returns was far lower than the market. He did this by exploiting market inefficiencies using warrants, options, and convertible bonds. The Kelly formula was for him a risk management discipline and not a direct source of excess return. </blockquote><br />
<br />
Shannon also made a lot of money on the stock market, but did not use Kelly's formula. In his [http://www.amazon.com/gp/product/customer-reviews/0809046377/ref=cm_cr_dp_pt/103-8647004-5865443?%5Fencoding=UTF8&n=283155&s=books review] Gaeton Lion writes<br />
<br />
<blockquote>Claude Shannon amassed large wealth by recording one of the best investment records. His performance had little to do with Kelly's formula. Between 1966 and 1986, his record beat even Warren Buffet (28% to 27% respectively). Shannon strategy was similar to Buffet. Both their stock portfolios were concentrated, and held for the long term. Shannon achieved his record by holding mainly three stocks (Teledyne, Motorola, and HP). The difference between the two was that Shannon invested in technology because he understood it well, while Buffet did not. </blockquote><br />
<br />
Finally, Thorp provided the following comments for the book cover:<br />
<br />
<blockquote>From bookies to billionaires, you'll meet a motley cast of characters in this highly original, 'outside the box' look at gambling and investing. Read it for the stories alone, and you'll be surprised at how much else you can learn without even trying. --Edward O. Thorp, author of ''Beat the Dealer'' and ''Beat the Market''.</blockquote><br />
<br />
Submitted by Laurie Snell.<br />
<br />
<br />
==Which foods prevent cancer?==<br />
<br />
Which of these foods will stop cancer? (Not so fast)<br><br />
New York Times, 27 September 2005, Sect. F, p. 1<Br><br />
Gina Kolata<br />
<br />
Among other examples, the article includes a [http://www.nytimes.com/imagepages/2005/09/26/science/20050927_CANCER_GRAPHIC.html data graphic] on purported benefits of dietary fiber in preventing colorectal cancer. Early observational studies indicated an association, but subsequent randomized experiments found no effect. <br />
<br />
More to follow.<br />
<br />
<br />
==Slices of risk and the <em>broken heart</em> concept==<br />
[http://www.gloriamundi.org/picsresources/news20050912.pdf How a Formula Ignited Market That Burned Some Big Investors],<br />
Mark Whitehouse, The Wall Street Journal, September 12, 2005.<br><br />
<br />
This on-line article relates how a statistician, David Li,<br />
unknown outside a small coterie of finance theorists, helped change the world of investing. <br />
<br />
The article focuses on a event last May when General Motors Corp's debt<br />
was downgraded to junk status, causing turmoil in some financial markets.<br />
The article gives a nice summary of the underlying financial instruments known<br />
as credit derivatives -<br />
investment contracts structured so their value depends on the behavior of some other thing or event -<br />
with exotic names like <br />
[http://en.wikipedia.org/wiki/Collateralized_debt_obligations collateralized debt obligations] and [http://en.wikipedia.org/wiki/Credit_default_swap credit-default swaps].<br />
<br />
The critical step is to estimate the likelihood that many of the companies <br />
in a pool of companies would go bust at once. <br />
For instance, if the companies were all in closely related industries,<br />
such as auto-parts suppliers, they might fall like dominoes after a catastrophic event.<br />
Such a pool would have a 'high default correlation'.<br />
<br />
In 1997, nobody knew how to calculate default correlations with any precision. <br />
Mr. Li's solution drew inspiration from a concept in actuarial science known as the <br />
<em>broken heart</em> syndrome - people tend to die faster after the death of a beloved spouse. <br />
Some of his colleagues from academia were working on a way to predict this<br />
death correlation, something quite useful to companies that sell life insurance and joint annuities.<br />
He says:<br />
<blockquote><br />
Suddenly I thought that the problem I was trying to solve was exactly like the problem these<br />
guys were trying to solve,.<br />
Default is like the death of a company, so we should<br />
model this the same way we model human life."<br />
</blockquote><br />
<br />
This gave him the idea of using [http://en.wikipedia.org/wiki/Copula_%28statistics%29 copulas], <br />
mathematical functions the colleagues had begun applying to actuarial science. <br />
Copulas help predict the likelihood of various events<br />
occurring when those events depend to some extent on one another. <br />
Until the events last May of this year, one of the most popular copulas for bond pools <br />
was the Gaussian copula, named after <br />
[http://en.wikipedia.org/wiki/Carl_Friedrich_Gauss Carl Friedrich Gauss], a 19th-century German statistician. <br />
<br />
===Further reading===<br />
* The [http://www.gloriamundi.org/picsresources/news20050912.pdf on-line article] gives more details about what went wrong in the financial markets in May and the search for a more appropriate copula to capture better the <em>broken heart</em> syndrome between companies.<br />
* [http://en.wikipedia.org/wiki/Wikipedia Wikipedia] is a very worthwhile on-line resource for definitions of technical words, such as [http://en.wikipedia.org/wiki/Copula_%28statistics%29 copula].<br />
<br />
Submitted by John Gavin.<br />
<br />
<br />
==Learning to speak via statistics and graph theory==<br />
<br />
[http://education.guardian.co.uk/tefl/teaching/story/0,15085,1576100,00.html Computer learns grammar by crunching sentences], Max de Lotbinière September 23, 2005, [http://www.guardianweekly.co.uk/ Guardian Weekly].<br><br />
[http://www.cornellsun.com/vnews/display.v/ART/2005/09/09/432118a84f6af Profs’ New Software ‘Learns’ Languages], Ben Birnbaum, 9 Sep 2005, Cornell Daily Sun.<br />
<br />
A language-learning robot may sound like science fiction but new software, developed by Cornell University psychology professor Shimon Edelman, with colleagues Zach Solan, David Horn and Eytan Ruppin from Tel Aviv University in Israel, is well on the way to constructing a computer program that can teach itself languages and make up its own sentences, the developers' claim.<br />
<br />
Unlike previous attempts at developing computer algorithms for language learning - "Automatic Distillation of Structure," or "ADIOS" for short - discovers complex patterns in raw text by repeatedly aligning sentences and looking for overlapping parts.<br />
Once it has derived a language's rules of grammar,<br />
it can then produce sentences of its own, simply from blocks of text in that language.<br />
<br />
It has been evaluated on artificial context-free grammars with thousands of rules, <br />
on natural languages as diverse as English and Chinese, <br />
on coding regions in DNA sequences and on protein data correlating sequence with function. <br />
<br />
Edelman comments:<br />
<blockquote><br />
Adios relies on a statistical method for pattern extraction and on structured generalisations <br />
- the two processes that have been implicated in language acquisition.<br />
Our experiments show that Adios can acquire intricate structures <br />
from raw data including transcripts of parents' speech directed at two- or three-year-olds.<br />
This may eventually help researchers understand how children, <br />
who learn language in a similar item-by-item fashion, and with little supervision, <br />
eventually master the full complexity of their native tongue.<br />
</blockquote><br />
<br />
[http://plus.maths.org/latestnews/may-aug05/adios/ Plus Magazine's website]<br />
offers a more logical explanation:<br />
<blockquote><br />
The ADIOS algorithm is based on statistical and algebraic methods performed on one of the most basic and versatile objects of mathematics - the graph.<br />
Given a text, the program loads it as a graph by representing each word by a node, or vertex, and each sentence by a sequence of nodes connected by lines. A string of words in the text is now represented by a path in the graph. <br><br />
<br />
Next it performs a statistical analysis to see which paths, or strings of words, occur unusually often. <br />
It then decides that those that appear most frequently - called "significant patterns" - <br />
can safely be regarded as a single unit<br />
and replaces the set of vertices in each of these patterns by a single vertex, <br />
thus creating a new, generalised, graph.<br><br />
<br />
Finally, the program looks for paths in the graph which just differ by one vertex. <br />
These stand for parts of sentences that just differ by one word (or compound of words) like "the cat is hungry" and "the dog is hungry". <br />
Performing another statistical test on the frequency of these paths, the program identifies classes of vertices, or words, that can be regarded as interchangeable, or equivalent. <br />
The sentence involved is legitimate no matter which of the words in the class - in our example "cat" or "dog" - you put in.<br><br />
<br />
This last step is then repeated recursively.<br><br />
</blockquote><br />
<br />
[http://plus.maths.org/latestnews/may-aug05/adios/ The website] uses graphs to illustrate some examples and it finishes with some reassuring words:<br />
<blockquote><br />
All this doesn't mean, of course, that the program actually "understands" what it's saying. It simply knows how to have a good go at piecing together fragments of sentences it has identified, in the hope that they are grammatically correct. So if, like me, you're prone to swearing at your computer, you can safely continue to do so: it won't answer back for a long while yet.<br />
</blockquote><br />
<br />
===Further reading===<br />
The [http://adios.tau.ac.il/ ADIOS homepage] offers an overview and more detailed description of the program.<br />
<br />
Submitted by John Gavin.<br />
<br />
==Understanding probability==<br />
<br />
Understanding Probability:Chance rules in everyday life<br><br />
Cambridge University Press 2004<br><br />
Henk Tijms<br />
<br />
Hank Tijms is Professor in Operation Research at the Vrije University in Amsterdam. This book is based on his earlier Dutch book “Spelen met Kansen.” <br />
<br />
The aim of this book is to show how probability applies to our everyday life in a way that your Uncle George could understand even if he has forgotten much of his high school math. Tijms does not try to avoid mathematics but only to postpone the formal math until the reader has seen the many applications of probability in the real world, how much fun it is, and learned to work problems and when he can’t work one how to get the answer by simulation. He learns all this in part I of the book and then he learns the more formal math in Part II.<br />
<br />
In Chapter 1 Tijms asks the reader to think about problems with surprising answers in the spirit of Susan Holmes “[http://www-stat.stanford.edu/~susan/surprise/ Probability by Surprise]” including the birthday problem and the Monty Hall problem. Readers are on their own to try to solve one or more of the problems but promised that they will see the solutions later in the book. <br />
<br />
Chapter 2 deals with the law of large numbers and introduces the concept of simulation. This theorem is explained and illustrated by problems related, for example, to coin tossing, random walks and casino games. Expected value is introduced in an informal way to be defined more carefully later in the book. For the reader who is not frightened by mathematical formulas, Tijms includes a discussion of the Kelly betting system with a footnote saying that this paragraph can be skipped at first reading. This is a fascinating topic that is widely applied in gambling and stock investment but rarely appears in a probability book.<br />
<br />
In Chapter 3 the author returns to previous problems such as the birthday problem and gambling systems and solves them first by simulation and then by mathematics. <br />
<br />
In this chapter Tijms describes Efron’s bootstrap method and uses it to solve a number of problems including a hypothetical clinical trial and to test if the famous 1970 draft lottery during the Vietnam War was fair. Again the bootstrap method has wide application but rarely occurs in an elementary probability or statistics book.<br />
<br />
Chapter 4 describes the binomial, Poisson, and hypergeomtric distributions and how to use them in solving problems such as the famous hat check problem, and a variety of interesting lottery questions. The Poisson process is discussed but again with the footnote that novice readers might want to read this at a later time.<br />
<br />
Chapter 5 is mainly about Center Limit Theorem and its many applications especially to statistics. <br />
<br />
Chapter 6 introduces Chance trees and Bayes’s rule. The tree method is used to explain a variety of problems including the Monty Hall Problem and the false-positive paradox. <br />
<br />
This is a brief description of the first six chapters which constitute Part I of the book. Now the fun is over. Part 2 called “Essentials of probability” looks like the traditional first chapters in a standard probability book. But the reader has already found how exciting probability is, has a good intuitive idea of the basic concepts and has worked many of the interesting problems at the end of each chapter either using math or simulation. For some students this might allow them to actually enjoy Part 2. But your Uncle George may want to quit while they are ahead. <br />
<br />
Tijms writes with great clarity and his enthusiasm for probability in the real world is contagious. We were delighted to see, as acknowledged in the preface, that Tijms included several of the more interesting problems discussed in Chance News, often going well beyond what we had said in our discussion of the problem. <br />
<br />
This book presents a completely new way to go about teaching a first course in probability and we think those who teach such a course should consider trying it out.<br />
<br />
===Discussion===<br />
<br />
(1) In the days of Basic we required all students to learn Basic in their first math course so we could assume that students could write programs to simulate probability problems and so me made heavy use of simulation as suggested in this book. The author uses Pascal in his book. What present language do you think is easiest for a student with no computing experience to learn?<br />
<br />
We asked Professor Tijms what the situation was in math departments in Europe and he replied:<br />
<br />
<blockquote>In math departments of universities and polytechnic schools in Europe students learn to write computer programs. In my university they still learn to program in Java and C++ ( in previous days Pascal), but I see in the Netherlands the trend that the instructors think it is sufficient if the students are able to program in Matlab. <br><br><br />
<br />
In ny book I have chosen to formulate the simulation programs in Pascal because of the clarity and the simplicity of the language, though this language is hardly used anymore. The introductory probability course at my university is given before they have learned to program, but this does not prevent them of simulating probability problems by using Excel. In the simulation of many elementary probability problems a random-number generator alone suffices to simulate those problems and so Excel can be used. In the second year they have mastered Matlab, a perfect tool with its excellent graphics to simulate many challenging probability problems ( they really like it, in particular when it concerns problems such as the problems 2.24-2.45 in chapter 2 and the problems 5.11-5.13 in chapter 5). <br />
</blockquote><br />
<br />
<br />
(2) Do you think that probability books should include data to test probability models that are said to describe real world problems? If so name some models that you think would pass such a test and some that you think might not.<br />
<br />
Submitted by Laurie Snell<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Societies worse off when they have God on their side==<br />
<br />
[http://www.timesonline.co.uk/article/0,,2-1798944,00.html Societies worse off when they have God on their side]<br><br />
Timesonline, September 27, 2005<br><br />
Ruth Gledhill<br />
<br />
[http://moses.creighton.edu/JRS/2005/2005-11.html Cross-national correlations of quantifiable societal health with popular religiosity and secularism in the prosperous democracies]<br><br />
Journal of Religion & Society, Vol.7(2005)<br><br />
Gregory S. Paul<br />
<br />
In the Times article we read:<br />
<br />
<blockquote>According to the study, belief in and worship of God are not only unnecessary for a healthy society but may actually contribute to social problems.<br><br><br />
Many liberal Christians and believers of other faiths hold that religious belief is socially beneficial, believing that it helps to lower rates of violent crime, murder, suicide, sexual promiscuity and abortion. The benefits of religious belief to a society have been described as its “spiritual capital”. But the study claims that the devotion of many in the US may actually contribute to its ills. <br />
</blockquote><br />
<br />
Gregory Paul is a dinosaur paleontologist and on an [http://www.abc.net.au/worldtoday/indexes/2005/twt_20050928.htm interview] on Australian ABC radio Paul said that, being a paleontologist, for many years he had to deal with the issue of creationism versus evolutionary science in the U.S and his interest in evolutionary science prompted him to look at whether there was any link between the religiosity of a society and how well that society functions. <br />
<br />
If you look at Paul's article you will find very little technical statistical analysis, for example, he did not carry out a regression analysis. Rather he rests his case on the series of scatterplots.<br />
<br />
Paul describes his data sources as:<br />
<br />
<blockquote>Data sources for rates of religious belief and practice as well as acceptance of evolution are the 1993 Environment I (Bishop) and 1998 Religion II polls conducted by the International Social Survey Program (ISSP), a cross-national collaboration on social science surveys using standard methodologies that currently involves 38 nations. The last survey interviewed approximately 23,000 people in almost all (17) of the developed democracies; Portugal is also plotted as an example of a second world European democracy. Results for western and eastern Germany are combined following the regions' populations. England is generally Great Britain excluding Northern Ireland; Holland is all of the Netherlands. The results largely agree with national surveys on the same subjects; for example, both ISSP and Gallup indicate that absolute plus less certain believers in a higher power are about 90% of the U.S. population. The plots include Bible literalism and frequency of prayer and service attendance, as well as absolute belief in a creator, in order to examine religiosity in terms of ardency, conservatism, and activities. </blockquote><br />
<br />
Here are the countries Paul considered with the abbreviations used on the graphics. <br />
<br />
A = Australia, C = Canada, D = Denmark, E = Great Britain, F = France, G = Germany,<br />
H = Holland, I = Ireland, J = Japan, L = Switzerland, N = Norway, P = Portugal, R = Austria,<br />
S = Spain, T = Italy, U = United States, W = Sweden, Z = New Zealand.<br />
<br />
There seems to be no agreement as to which countries are developed democracies. For example Paul might have included Greece and Belgium, Finland, and others but the data may have determined his choice. Paul comments that he added Portugal as an example of a second world democracy. <br />
<br />
Paul's anaysis of the data includes a series of 9 Figures which are available at the end of the article and are the most interesting part of the study. If you try printing Paul's article you will only get the first of his 9 Figures. When you look at the [http://moses.creighton.edu/JRS/2005/2005-11.html web version] you will still see only Figure 1 but the others can be viewed by selecting the numbers from 2 to 9 on the left side of Figure 1.<br />
<br />
Figure 1 deals with the proportion of people who accept human evolution which is interesting but not as relevant to the welfare of the people as others so we will look at Figure 2.<br />
<br />
[[Image:religion2.png|500px|center|Source:Gregory Paul]]<br />
<br />
Each Figure iprovides 5 separate scatterplots. Ïn Figure 2 we see that the U.S. has largest number--between 6 and 7-- of homicides per 100,000 and Spain has the lowest number with less than 1 homicide per 100,000. We also see that the U.S. has the highest proportion of people, about 25%, who take the bible literally while several countries have less than 10% such people.<br />
<br />
What we cannot do is compare the number of homicides per thousand between those who take the bible literally and those who are agnostics or atheists which is what we would really want to know. Presumably the data did not permit this comparison. <br />
<br />
[[Image:religion3.png|500px|center|Source:Gregory Paul]]<br />
<br />
Figure 3 deals with "14-24 year old suicides per 100,000". Here the U.S. is in about the middle.<br />
<br />
Figure 4 deals with the "under-five mortalities per 1000 births".<br />
<br />
[[Image:religion4.png|500px|center|Source:Gregory Paul]]<br />
<br />
Ignoring Portugal, the U.S. has the highest number of under-five mortalities per 1000 births-- between 7 and--8 while several countries have only 4.<br />
<br />
The other figures can be seen at end of Paul's article. They deal with life expectancy, sexually transmitted diseases, abortion and 15-16 year old pregnancies. Life expectancy is the smallest in the U.S. and for sexually transmitted diseases, abortion and 15-17 year old prenacies the U.S. is at the top of the graphs and in fact these look like outliers.<br />
<br />
Well, this study does not by itself justify the Times hedline: "Societies worse off when they have God on their side." Paul himself would not claim this. He writes:<br />
<br />
<blockquote> This study is a first, brief look at an important subject that has been almost entirely neglected by social scientists. The primary intent is to present basic correlations of the elemental data. Some conclusions that can be gleaned from the plots are outlined. This is not an attempt to present a definitive study that establishes cause versus effect between religiosity, secularism and societal health. It is hoped that these original correlations and results will spark future research and debate on the issue.</block<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div></div>Nano12https://www.causeweb.org/wiki/chance/index.php?title=How_to_submit_a_new_article_or_edit_an_existing_article&diff=1569How to submit a new article or edit an existing article2005-11-05T09:33:29Z<p>Nano12: </p>
<hr />
<div>The basic item in a Wiki is a page which has its own URL. Each Chance News issue consists of a sequence of items all on the same Wiki page. To add a new item, choose the current issue and choose edit from the top of the page. Then add at the bottom of the existing text add ==foo== where foo is the name of your item. This can, but does not have to be. the name of the article you are discussing. This will automatically add "foo" to the table of contents. The table of contents cannot be changed accept by adding or removing an article. (It will not be visible until their are at least 4 items added to the Chance News).<br />
<br />
Then, while still in edit mode, type in your discussion of the article. When you are in the "edit" mode you will see "Show preview" and "Save page" at the bottom of the article. At any time you can choose "Show preview" to see if you are happy with what your have written. If so go back to the bottom of the page and choose "Save page". You must choose "Save page" before leaving the edit mode to save a change you have made.<br />
<br />
Some prowsers have a limit to how big a Chance News can be. If you find, when in edit mode, that your browser will not accept more text you can go to the Main Page and add the next issue of Chance News by editting the main page. Then put your article as the first article in this new issue of Chance News.<br />
<br />
To change an existing article, select the article from the table of contents, choose "edit" from the top of the article and make your changes. This might incuded new discussion questions. Use "Show preview" and "Save page" the same way you would for adding an article. <br />
<br />
The "history" item at the top of a page allows you to see previous versions of an article. You can revert to a previous version by clicking on it and then chossing "Save page."<br />
<br />
In the Summary box at the bottom of a page you can add the name of our article or indicate the type of change you made. <br />
<br />
For help in editing a page, including how to add pictures, links, special characters, etc., choose "Help" from the side box. You can also see how to do these by looking at the edit version of previous articles. For example you will see that a format for adding a centered image is<br />
<br />
[[Image:Shiller1.jpg|500px|center|Source:Shiller:Irational Exuberance]]<br />
<br />
This makes the image Shiller1.jpg of size 400 pixels centered and with the source as indicated. It is recommended that you limit the size to 400 pixels but you might be able to go to 500 pixels.<br />
<br />
Copyright. Since, in most cases, we are doing a critical analysis of an article, fair use should allow us to make reasonable quotes, graphics, images etc. from the article without the permission of the copyright owner. However, you should indicate the source. You can read one lawyer's interpretation of fair use as it applies to Chance News [http://www.dartmouth.edu/~chance/Fair_Use/fair.html here]. When you upload an image you will be asked to indicate if you are doing it under fair use or you have permission from the copyright owner and also to give the source. <br />
<br />
Feel free to add "submitted by "your name" at the top or bottom of your article if you wish.<br />
<br />
Good luck and remember it will be easier next time!<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div></div>Nano12https://www.causeweb.org/wiki/chance/index.php?title=Chance_News_7&diff=1540Chance News 72005-11-05T09:33:22Z<p>Nano12: /* Societies worse off when they have God on their side */</p>
<hr />
<div>Sept 26 2005 to Oct 15 2005<br />
==Quotation==<br />
<blockquote><br />
While writing my book [Stochastic Processes] I had an argument with Feller [Introuction to Probability Theory and its Applications]. He asserted that everyone said "random variable" and I asserted that everyone said "chance variable." We obviously had to use the same name in our books, so we decided the issue by a stochastic procedure. That is, we tossed for it and he won. </blockquote><br />
<br />
<p align = right> Joe Doob<br><br />
[http://www.dartmouth.edu/~chance/Doob/conversation.html Statistical Science]<br><br />
<br />
==Forsooth==<br />
<br />
Peter Winkler suggested our first forsooth.<br />
<br />
<blockquote>Texas beats Ohio State in their opening game <br />
of the season (Saturday Sept 10 2002). The sportscasters (legendary Brent Musburger on play-by-play or Gary Danielson on analysis) observed that of the 14 teams who have <br />
previously played in the championship game (at the end of each season) 5 <br />
have suffered an earlier defeat. "Thus," they conclude, "Ohio State can <br />
still make it to the championship game, but their chances are now less <br />
than 50%."</blockquote><br />
<br />
===Discussion===<br />
<br />
What is wrong with this?<br />
----<br />
Here are forsooths from the September 2005 issues of RSS NEWS<br />
<br />
<blockquote>'Big ticket quiz' at the start of Wimbledon:<br><br><br />
Q. How many punnets (a small light basket or other container for fruit or vegetables) of strawberries are eaten each day during the Wimbledon tournament?<br><br />
Is it (a) over 8,000, (b) over 9,000 or (c) over 10,000?</blockquote><br />
<br />
<div align="right">BBC radio 5<br><br />
20 June 2005</div><br />
<br />
<blockquote>Waiting time for foot surgery down by 500%</blockquote><br />
<br />
<div align="right">Evening News (Edinburgh)<br><br />
5 July 2005</div><br />
<br />
The next two forsooths are from the October RSS news.<br />
<br />
<blockquote>In 1996-8 when the number attending university was static, the participation of women was also static, but male participation fell.</blockquote><br />
<br />
<div align="right">The Times Higher<br><br />
21 January 2005</div><br />
<br />
<blockquote>[On the subject of congestion on the London Underground..] 'Last year 976 million of us used the tube...'</blockquote><br />
<br />
<div align="right">BBC London News<br><br />
19 May 2005</div><br />
<br />
<br />
==Fortune's Formula==<br />
<br />
''Fortune's Formula: Wanna Bet?''<br><br />
''New York Times Book Section'', September 25, 2005<br><br />
David Pogue<br />
<br />
This must be the kind of review that every Science writer dreams of. Pogue ends his review with:<br />
<br />
<blockquote> ''Fortune's Formula'' may be the world's first history book, gambling primer, mathematics text, economics manual, personal finance guide and joke book in a single volume. Poundstone comes across like the best college professor you ever had, someone who can turn almost any technical topic into an entertaining and zesty lecture. But every now and then, you can't help wishing there were some teaching assistants on hand to help.</blockquote><br />
<br />
The author William Poundstone is a science writer who has written a number of very successful science books. His book, ''Prisoner's dilemma: John von Neumann, game theory and the puzzle of the bomb'', was written in the style of this book. Indeed Helen Joyce, in her review of this book in Plus Magazine writes:<br />
<br />
<blockquote>This book is a curious mixture of biography, history and mathematics, all neatly packaged into an entertaining and enlightening read. </blockquote><br />
<br />
Poundstone describes himself as a visual artist who does books as a "day job.". You can learn about his art work [http://www.uiowa.edu/~iareview/tirweb/feature/poundstone/interview2.htm here].<br />
<br />
''Fortune's Formula'' is primarily the story of Edward Thorp, Claude Shannon, and John Kelly and their attempt to use mathematics to make money gambling in casinos and on the stock market. None of these did their graduate work in mathematics. Thorp and Kelly got their Phd's in physics and Shannon in Genetics. <br />
<br />
In the spring of 1955, while a graduate student at UCLA, Thorp joined a discussion on the possiblity of making money from roulette. Thorp suggested that they could taking advantage of the fact that bets are still accepted for a few second after the croupier releases the ball, and in these seconds, he could estimate what part of the wheel the ball would stop. <br />
<br />
Thorp did not pursue this and in 1959 became an instructor in mathematics at M.I.T. Here he became interested in blackjack and developed his famous card counting method for wining at blackjack. He decided to publish his method in the most prestigious journal he could find and settled on ''Proceedings of the National Academy of Sciences''. For this he needed to have a member of the Academy submit his paper. The only member in the math department was Shannon so he had to persuade him of the importance of his paper. Shannon not only agreed but in the process became fascinated by Thorp's idea for beating roulette. He agreed to help Thorp carry this out. They built a roulette machine in Shannon's basement. It worked fine there in trial runs but not so well in the casino so they did not pursue this method of getting rich. <br />
<br />
Of course Thorp is best known for showing that blackjack is a favorable game and giving a method to exploit this fact. Shannon is best known for his work in information theory. Kelly is known his method for gambling in a favorable game. This plays a central role in Poundstone's book and is probably why Pogue felt that it would help if he had a teaching assistant. Poundstone tries to explain Kelly's work in many different ways but what he really needed to understand it is an example but this required too many formulas for a popular book. So we shall include an example from Chance News 7.09. <br />
<br />
Writing for Motley Fool, 3 April 1997 Mark Brady complained about the inumeracy of the general public and gave a number of examples including this one:<br />
<br />
<blockquote> Fear of uncertainty and innumeracy are synergistic. Most people cannot do the odds. What is a better deal over a year? A 100% safe return with 5 percent interest or a 90 percent safe return with a 20 percent return. For the first deal, your return will be 5% percent. For the second, your return will be 8%. Say you invest $1000 10 times. Your interest for the 9 successful deals will be 9000 x 0.2 or 1800. Subtract the 1000 you lost on the 10th deal and you get a $800 return on your original $10,000 for 8 percent.</blockquote><br />
<br />
Peter Doyle suggested that a better investment strategy in this case is:<br />
<br />
Faced with a 100 percent-safe investment returning 5 percent and a 90 percent-safe investment returning 20%, you should invest 20% of your funds in the risky investment and 80% in the safe investment. This gives you an effective return of roughly 5.31962607969968292 percent. <br />
<br />
Peter is using a money management system due to J. L. Kelly (1956: "A new interpretation of information rate," ''Bell System Technical Journal'', '''35'''). Kelly was interested in finding a rational way to invest your money faced with one or more investment schemes, each of which has a positive expected gain. He did not think it reasonable to try simply to maximize your expected return. If you did this in the Motley Fools example as suggested by Mark Brady, you would choose the risky investment and might well lose all your money the first year. We will illustrate what Kelly did propose in terms of Motley Fools example. <br />
<br />
We start with an initial capital, which we choose for convenience to be $1, and invest a fraction r of this money in the gamble and a fraction 1-r in the sure-thing. Then for the next year we use the same fractions to invest the money that resulted from the first year's investments and continue, using the same r each year. Assume, for example, that in the first and third years we win the gamble and in the second year we lose it. Then after 3 years our investment returns an amount f(r) where: <br />
<br />
<math><br />
f(r) = (1.2r + 1.05(1-r))(1.05(1-r))(1.2r + 1.05(1-r)). <br />
</math><br />
<br />
After n years, we would have n such factors, each corresponding to a win or a loss of our risky investment. Since the order of the terms does not matter our capital will be: <br />
<br />
<math><br />
f(r,n) = (1.2r + 1.05(1-r))^W(1.05(1-r))^L<br />
</math><br />
<br />
where W is the number of times we won the risky investment and L the number of times we lost it. Now Kelly calls the quantity:<br />
<br />
<math><br />
G(r) =\lim_{n \to \infty }\frac{\log(f( r,n)} {n}<br />
</math> <br />
<br />
the exponential rate of growth of our capital. In terms of G(r) our capital should grow like <math> e^{G(r)} </math>. In our example: <br />
<br />
<math><br />
\log(\frac{f(r,n)}{n}) = \frac{W}{n}\log(1.2r + 1.05(1-r)) + \frac{L}{n}\log(1.05(1-r))<br />
</math> <br />
<br />
Since we have a 90% chance of winning our gamble, the [http://en.wikipedia.org/wiki/Strong_law_of_large_numbers#The_strong_law strong law of large numbers] tells us that as n tends to infinity this will converge to <br />
<br />
<math><br />
G(r) = 0.9\log(1.2r + 1.05(1-r))+0.1\log(1.05(1-r))<br />
</math><br />
<br />
It is a simple calculus problem to show that G(r) is maximized by r = 0.2 with: <br />
G(0.2) = 0.05183. Then e^{0.05183} = 1.0532, showing that our maximum rate of growth is 5.32% as claimed by Peter. <br />
<br />
The attractiveness of the Kelly investment scheme is that, in the long run, any other investment strategy (including those where you are allowed to change your investment proportions at different times) will do less well. "In the long run and less well" means more precisely that the ratio of your return under the Kelly scheme and your return under any other strategy will tend to infinity.<br />
<br />
Thorp had a very good experience in the stock market, which is described very well by Gaeton Lion in his excellent [http://www.amazon.com/gp/product/customer-reviews/0809046377/ref=cm_cr_dp_pt/103-8647004-5865443?%5Fencoding=UTF8&n=283155&s=books review] of ''Fortune's Formula''. He writes:<br />
<br />
<blockquote> Ed Thorp succeeded in deriving superior returns in both gambling and investing. But, it was not so much because of Kelly's formula. He developed other tools to achieve superior returns. In gambling, Ed Thorp succeeded at Black Jack by developing the card counting method. He just used intuitively Kelly's formula to increase his bets whenever the odds were in his favor. Later, he ran a hedge fund for 20 years until the late 80s and earned a rate of return of 14% handily beating the market's 8% during the period. <br><br><br />
<br />
Also, his hedge fund hardly lost any value on black Monday in October 1987, when the market crashed by 22%. The volatility of his returns was far lower than the market. He did this by exploiting market inefficiencies using warrants, options, and convertible bonds. The Kelly formula was for him a risk management discipline and not a direct source of excess return. </blockquote><br />
<br />
Shannon also made a lot of money on the stock market, but did not use Kelly's formula. In his [http://www.amazon.com/gp/product/customer-reviews/0809046377/ref=cm_cr_dp_pt/103-8647004-5865443?%5Fencoding=UTF8&n=283155&s=books review] Gaeton Lion writes<br />
<br />
<blockquote>Claude Shannon amassed large wealth by recording one of the best investment records. His performance had little to do with Kelly's formula. Between 1966 and 1986, his record beat even Warren Buffet (28% to 27% respectively). Shannon strategy was similar to Buffet. Both their stock portfolios were concentrated, and held for the long term. Shannon achieved his record by holding mainly three stocks (Teledyne, Motorola, and HP). The difference between the two was that Shannon invested in technology because he understood it well, while Buffet did not. </blockquote><br />
<br />
Finally, Thorp provided the following comments for the book cover:<br />
<br />
<blockquote>From bookies to billionaires, you'll meet a motley cast of characters in this highly original, 'outside the box' look at gambling and investing. Read it for the stories alone, and you'll be surprised at how much else you can learn without even trying. --Edward O. Thorp, author of ''Beat the Dealer'' and ''Beat the Market''.</blockquote><br />
<br />
Submitted by Laurie Snell.<br />
<br />
<br />
==Which foods prevent cancer?==<br />
<br />
Which of these foods will stop cancer? (Not so fast)<br><br />
New York Times, 27 September 2005, Sect. F, p. 1<Br><br />
Gina Kolata<br />
<br />
Among other examples, the article includes a [http://www.nytimes.com/imagepages/2005/09/26/science/20050927_CANCER_GRAPHIC.html data graphic] on purported benefits of dietary fiber in preventing colorectal cancer. Early observational studies indicated an association, but subsequent randomized experiments found no effect. <br />
<br />
More to follow.<br />
<br />
<br />
==Slices of risk and the <em>broken heart</em> concept==<br />
[http://www.gloriamundi.org/picsresources/news20050912.pdf How a Formula Ignited Market That Burned Some Big Investors],<br />
Mark Whitehouse, The Wall Street Journal, September 12, 2005.<br><br />
<br />
This on-line article relates how a statistician, David Li,<br />
unknown outside a small coterie of finance theorists, helped change the world of investing. <br />
<br />
The article focuses on a event last May when General Motors Corp's debt<br />
was downgraded to junk status, causing turmoil in some financial markets.<br />
The article gives a nice summary of the underlying financial instruments known<br />
as credit derivatives -<br />
investment contracts structured so their value depends on the behavior of some other thing or event -<br />
with exotic names like <br />
[http://en.wikipedia.org/wiki/Collateralized_debt_obligations collateralized debt obligations] and [http://en.wikipedia.org/wiki/Credit_default_swap credit-default swaps].<br />
<br />
The critical step is to estimate the likelihood that many of the companies <br />
in a pool of companies would go bust at once. <br />
For instance, if the companies were all in closely related industries,<br />
such as auto-parts suppliers, they might fall like dominoes after a catastrophic event.<br />
Such a pool would have a 'high default correlation'.<br />
<br />
In 1997, nobody knew how to calculate default correlations with any precision. <br />
Mr. Li's solution drew inspiration from a concept in actuarial science known as the <br />
<em>broken heart</em> syndrome - people tend to die faster after the death of a beloved spouse. <br />
Some of his colleagues from academia were working on a way to predict this<br />
death correlation, something quite useful to companies that sell life insurance and joint annuities.<br />
He says:<br />
<blockquote><br />
Suddenly I thought that the problem I was trying to solve was exactly like the problem these<br />
guys were trying to solve,.<br />
Default is like the death of a company, so we should<br />
model this the same way we model human life."<br />
</blockquote><br />
<br />
This gave him the idea of using [http://en.wikipedia.org/wiki/Copula_%28statistics%29 copulas], <br />
mathematical functions the colleagues had begun applying to actuarial science. <br />
Copulas help predict the likelihood of various events<br />
occurring when those events depend to some extent on one another. <br />
Until the events last May of this year, one of the most popular copulas for bond pools <br />
was the Gaussian copula, named after <br />
[http://en.wikipedia.org/wiki/Carl_Friedrich_Gauss Carl Friedrich Gauss], a 19th-century German statistician. <br />
<br />
===Further reading===<br />
* The [http://www.gloriamundi.org/picsresources/news20050912.pdf on-line article] gives more details about what went wrong in the financial markets in May and the search for a more appropriate copula to capture better the <em>broken heart</em> syndrome between companies.<br />
* [http://en.wikipedia.org/wiki/Wikipedia Wikipedia] is a very worthwhile on-line resource for definitions of technical words, such as [http://en.wikipedia.org/wiki/Copula_%28statistics%29 copula].<br />
<br />
Submitted by John Gavin.<br />
<br />
<br />
==Learning to speak via statistics and graph theory==<br />
<br />
[http://education.guardian.co.uk/tefl/teaching/story/0,15085,1576100,00.html Computer learns grammar by crunching sentences], Max de Lotbinière September 23, 2005, [http://www.guardianweekly.co.uk/ Guardian Weekly].<br><br />
[http://www.cornellsun.com/vnews/display.v/ART/2005/09/09/432118a84f6af Profs’ New Software ‘Learns’ Languages], Ben Birnbaum, 9 Sep 2005, Cornell Daily Sun.<br />
<br />
A language-learning robot may sound like science fiction but new software, developed by Cornell University psychology professor Shimon Edelman, with colleagues Zach Solan, David Horn and Eytan Ruppin from Tel Aviv University in Israel, is well on the way to constructing a computer program that can teach itself languages and make up its own sentences, the developers' claim.<br />
<br />
Unlike previous attempts at developing computer algorithms for language learning - "Automatic Distillation of Structure," or "ADIOS" for short - discovers complex patterns in raw text by repeatedly aligning sentences and looking for overlapping parts.<br />
Once it has derived a language's rules of grammar,<br />
it can then produce sentences of its own, simply from blocks of text in that language.<br />
<br />
It has been evaluated on artificial context-free grammars with thousands of rules, <br />
on natural languages as diverse as English and Chinese, <br />
on coding regions in DNA sequences and on protein data correlating sequence with function. <br />
<br />
Edelman comments:<br />
<blockquote><br />
Adios relies on a statistical method for pattern extraction and on structured generalisations <br />
- the two processes that have been implicated in language acquisition.<br />
Our experiments show that Adios can acquire intricate structures <br />
from raw data including transcripts of parents' speech directed at two- or three-year-olds.<br />
This may eventually help researchers understand how children, <br />
who learn language in a similar item-by-item fashion, and with little supervision, <br />
eventually master the full complexity of their native tongue.<br />
</blockquote><br />
<br />
[http://plus.maths.org/latestnews/may-aug05/adios/ Plus Magazine's website]<br />
offers a more logical explanation:<br />
<blockquote><br />
The ADIOS algorithm is based on statistical and algebraic methods performed on one of the most basic and versatile objects of mathematics - the graph.<br />
Given a text, the program loads it as a graph by representing each word by a node, or vertex, and each sentence by a sequence of nodes connected by lines. A string of words in the text is now represented by a path in the graph. <br><br />
<br />
Next it performs a statistical analysis to see which paths, or strings of words, occur unusually often. <br />
It then decides that those that appear most frequently - called "significant patterns" - <br />
can safely be regarded as a single unit<br />
and replaces the set of vertices in each of these patterns by a single vertex, <br />
thus creating a new, generalised, graph.<br><br />
<br />
Finally, the program looks for paths in the graph which just differ by one vertex. <br />
These stand for parts of sentences that just differ by one word (or compound of words) like "the cat is hungry" and "the dog is hungry". <br />
Performing another statistical test on the frequency of these paths, the program identifies classes of vertices, or words, that can be regarded as interchangeable, or equivalent. <br />
The sentence involved is legitimate no matter which of the words in the class - in our example "cat" or "dog" - you put in.<br><br />
<br />
This last step is then repeated recursively.<br><br />
</blockquote><br />
<br />
[http://plus.maths.org/latestnews/may-aug05/adios/ The website] uses graphs to illustrate some examples and it finishes with some reassuring words:<br />
<blockquote><br />
All this doesn't mean, of course, that the program actually "understands" what it's saying. It simply knows how to have a good go at piecing together fragments of sentences it has identified, in the hope that they are grammatically correct. So if, like me, you're prone to swearing at your computer, you can safely continue to do so: it won't answer back for a long while yet.<br />
</blockquote><br />
<br />
===Further reading===<br />
The [http://adios.tau.ac.il/ ADIOS homepage] offers an overview and more detailed description of the program.<br />
<br />
Submitted by John Gavin.<br />
<br />
==Understanding probability==<br />
<br />
Understanding Probability:Chance rules in everyday life<br><br />
Cambridge University Press 2004<br><br />
Henk Tijms<br />
<br />
Hank Tijms is Professor in Operation Research at the Vrije University in Amsterdam. This book is based on his earlier Dutch book “Spelen met Kansen.” <br />
<br />
The aim of this book is to show how probability applies to our everyday life in a way that your Uncle George could understand even if he has forgotten much of his high school math. Tijms does not try to avoid mathematics but only to postpone the formal math until the reader has seen the many applications of probability in the real world, how much fun it is, and learned to work problems and when he can’t work one how to get the answer by simulation. He learns all this in part I of the book and then he learns the more formal math in Part II.<br />
<br />
In Chapter 1 Tijms asks the reader to think about problems with surprising answers in the spirit of Susan Holmes “[http://www-stat.stanford.edu/~susan/surprise/ Probability by Surprise]” including the birthday problem and the Monty Hall problem. Readers are on their own to try to solve one or more of the problems but promised that they will see the solutions later in the book. <br />
<br />
Chapter 2 deals with the law of large numbers and introduces the concept of simulation. This theorem is explained and illustrated by problems related, for example, to coin tossing, random walks and casino games. Expected value is introduced in an informal way to be defined more carefully later in the book. For the reader who is not frightened by mathematical formulas, Tijms includes a discussion of the Kelly betting system with a footnote saying that this paragraph can be skipped at first reading. This is a fascinating topic that is widely applied in gambling and stock investment but rarely appears in a probability book.<br />
<br />
In Chapter 3 the author returns to previous problems such as the birthday problem and gambling systems and solves them first by simulation and then by mathematics. <br />
<br />
In this chapter Tijms describes Efron’s bootstrap method and uses it to solve a number of problems including a hypothetical clinical trial and to test if the famous 1970 draft lottery during the Vietnam War was fair. Again the bootstrap method has wide application but rarely occurs in an elementary probability or statistics book.<br />
<br />
Chapter 4 describes the binomial, Poisson, and hypergeomtric distributions and how to use them in solving problems such as the famous hat check problem, and a variety of interesting lottery questions. The Poisson process is discussed but again with the footnote that novice readers might want to read this at a later time.<br />
<br />
Chapter 5 is mainly about Center Limit Theorem and its many applications especially to statistics. <br />
<br />
Chapter 6 introduces Chance trees and Bayes’s rule. The tree method is used to explain a variety of problems including the Monty Hall Problem and the false-positive paradox. <br />
<br />
This is a brief description of the first six chapters which constitute Part I of the book. Now the fun is over. Part 2 called “Essentials of probability” looks like the traditional first chapters in a standard probability book. But the reader has already found how exciting probability is, has a good intuitive idea of the basic concepts and has worked many of the interesting problems at the end of each chapter either using math or simulation. For some students this might allow them to actually enjoy Part 2. But your Uncle George may want to quit while they are ahead. <br />
<br />
Tijms writes with great clarity and his enthusiasm for probability in the real world is contagious. We were delighted to see, as acknowledged in the preface, that Tijms included several of the more interesting problems discussed in Chance News, often going well beyond what we had said in our discussion of the problem. <br />
<br />
This book presents a completely new way to go about teaching a first course in probability and we think those who teach such a course should consider trying it out.<br />
<br />
===Discussion===<br />
<br />
(1) In the days of Basic we required all students to learn Basic in their first math course so we could assume that students could write programs to simulate probability problems and so me made heavy use of simulation as suggested in this book. The author uses Pascal in his book. What present language do you think is easiest for a student with no computing experience to learn?<br />
<br />
We asked Professor Tijms what the situation was in math departments in Europe and he replied:<br />
<br />
<blockquote>In math departments of universities and polytechnic schools in Europe students learn to write computer programs. In my university they still learn to program in Java and C++ ( in previous days Pascal), but I see in the Netherlands the trend that the instructors think it is sufficient if the students are able to program in Matlab. <br><br><br />
<br />
In ny book I have chosen to formulate the simulation programs in Pascal because of the clarity and the simplicity of the language, though this language is hardly used anymore. The introductory probability course at my university is given before they have learned to program, but this does not prevent them of simulating probability problems by using Excel. In the simulation of many elementary probability problems a random-number generator alone suffices to simulate those problems and so Excel can be used. In the second year they have mastered Matlab, a perfect tool with its excellent graphics to simulate many challenging probability problems ( they really like it, in particular when it concerns problems such as the problems 2.24-2.45 in chapter 2 and the problems 5.11-5.13 in chapter 5). <br />
</blockquote><br />
<br />
<br />
(2) Do you think that probability books should include data to test probability models that are said to describe real world problems? If so name some models that you think would pass such a test and some that you think might not.<br />
<br />
Submitted by Laurie Snell<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Societies worse off when they have God on their side==<br />
<br />
[http://www.timesonline.co.uk/article/0,,2-1798944,00.html Societies worse off when they have God on their side]<br><br />
Timesonline, September 27, 2005<br><br />
Ruth Gledhill<br />
<br />
[http://moses.creighton.edu/JRS/2005/2005-11.html Cross-national correlations of quantifiable societal health with popular religiosity and secularism in the prosperous democracies]<br><br />
Journal of Religion & Society, Vol.7(2005)<br><br />
Gregory S. Paul<br />
<br />
In the Times article we read:<br />
<br />
<blockquote>According to the study, belief in and worship of God are not only unnecessary for a healthy society but may actually contribute to social problems.<br><br><br />
Many liberal Christians and believers of other faiths hold that religious belief is socially beneficial, believing that it helps to lower rates of violent crime, murder, suicide, sexual promiscuity and abortion. The benefits of religious belief to a society have been described as its “spiritual capital”. But the study claims that the devotion of many in the US may actually contribute to its ills. <br />
</blockquote><br />
<br />
Gregory Paul is a dinosaur paleontologist and on an [http://www.abc.net.au/worldtoday/indexes/2005/twt_20050928.htm interview] on Australian ABC radio Paul said that, being a paleontologist, for many years he had to deal with the issue of creationism versus evolutionary science in the U.S and his interest in evolutionary science prompted him to look at whether there was any link between the religiosity of a society and how well that society functions. <br />
<br />
If you look at Paul's article you will find very little technical statistical analysis, for example, he did not carry out a regression analysis. Rather he rests his case on the series of scatterplots.<br />
<br />
Paul describes his data sources as:<br />
<br />
<blockquote>Data sources for rates of religious belief and practice as well as acceptance of evolution are the 1993 Environment I (Bishop) and 1998 Religion II polls conducted by the International Social Survey Program (ISSP), a cross-national collaboration on social science surveys using standard methodologies that currently involves 38 nations. The last survey interviewed approximately 23,000 people in almost all (17) of the developed democracies; Portugal is also plotted as an example of a second world European democracy. Results for western and eastern Germany are combined following the regions' populations. England is generally Great Britain excluding Northern Ireland; Holland is all of the Netherlands. The results largely agree with national surveys on the same subjects; for example, both ISSP and Gallup indicate that absolute plus less certain believers in a higher power are about 90% of the U.S. population. The plots include Bible literalism and frequency of prayer and service attendance, as well as absolute belief in a creator, in order to examine religiosity in terms of ardency, conservatism, and activities. </blockquote><br />
<br />
Here are the countries Paul considered with the abbreviations used on the graphics. <br />
<br />
A = Australia, C = Canada, D = Denmark, E = Great Britain, F = France, G = Germany,<br />
H = Holland, I = Ireland, J = Japan, L = Switzerland, N = Norway, P = Portugal, R = Austria,<br />
S = Spain, T = Italy, U = United States, W = Sweden, Z = New Zealand.<br />
<br />
There seems to be no agreement as to which countries are developed democracies. For example Paul might have included Greece and Belgium, Finland, and others but the data may have determined his choice. Paul comments that he added Portugal as an example of a second world democracy. <br />
<br />
Paul's anaysis of the data includes a series of 9 Figures which are available at the end of the article and are the most interesting part of the study. If you try printing Paul's article you will only get the first of his 9 Figures. When you look at the [http://moses.creighton.edu/JRS/2005/2005-11.html web version] you will still see only Figure 1 but the others can be viewed by selecting the numbers from 2 to 9 on the left side of Figure 1.<br />
<br />
Figure 1 deals with the proportion of people who accept human evolution which is interesting but not as relevant to the welfare of the people as others so we will look at Figure 2.<br />
<br />
[[Image:religion2.png|500px|center|Source:Gregory Paul]]<br />
<br />
Each Figure iprovides 5 separate scatterplots. Ïn Figure 2 we see that the U.S. has largest number--between 6 and 7-- of homicides per 100,000 and Spain has the lowest number with less than 1 homicide per 100,000. We also see that the U.S. has the highest proportion of people, about 25%, who take the bible literally while several countries have less than 10% such people.<br />
<br />
What we cannot do is compare the number of homicides per thousand between those who take the bible literally and those who are agnostics or atheists which is what we would really want to know. Presumably the data did not permit this comparison. <br />
<br />
[[Image:religion3.png|500px|center|Source:Gregory Paul]]<br />
<br />
Figure 3 deals with "14-24 year old suicides per 100,000". Here the U.S. is in about the middle.<br />
<br />
Figure 4 deals with the "under-five mortalities per 1000 births".<br />
<br />
[[Image:religion4.png|500px|center|Source:Gregory Paul]]<br />
<br />
Ignoring Portugal, the U.S. has the highest number of under-five mortalities per 1000 births-- between 7 and--8 while several countries have only 4.<br />
<br />
The other figures can be seen at end of Paul's article. They deal with life expectancy, sexually transmitted diseases, abortion and 15-16 year old pregnancies. Life expectancy is the smallest in the U.S. and for sexually transmitted diseases, abortion and 15-17 year old prenacies the U.S. is at the top of the graphs and in fact these look like outliers.<br />
<br />
Well, this study does not by itself justify the Times hedline: "Societies worse off when they have God on their side." Paul himself would not claim this. He writes:<br />
<br />
<blockquote> This study is a first, brief look at an important subject that has been almost entirely neglected by social scientists. The primary intent is to present basic correlations of the elemental data. Some conclusions that can be gleaned from the plots are outlined. This is not an attempt to present a definitive study that establishes cause versus effect between religiosity, secularism and societal health. It is hoped that these original correlations and results will spark future research and debate on the issue.</block<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div></div>Nano12https://www.causeweb.org/wiki/chance/index.php?title=Chance_News_7&diff=1537Chance News 72005-11-05T09:33:15Z<p>Nano12: /* Discussion */</p>
<hr />
<div>Sept 26 2005 to Oct 15 2005<br />
==Quotation==<br />
<blockquote><br />
While writing my book [Stochastic Processes] I had an argument with Feller [Introuction to Probability Theory and its Applications]. He asserted that everyone said "random variable" and I asserted that everyone said "chance variable." We obviously had to use the same name in our books, so we decided the issue by a stochastic procedure. That is, we tossed for it and he won. </blockquote><br />
<br />
<p align = right> Joe Doob<br><br />
[http://www.dartmouth.edu/~chance/Doob/conversation.html Statistical Science]<br><br />
<br />
==Forsooth==<br />
<br />
Peter Winkler suggested our first forsooth.<br />
<br />
<blockquote>Texas beats Ohio State in their opening game <br />
of the season (Saturday Sept 10 2002). The sportscasters (legendary Brent Musburger on play-by-play or Gary Danielson on analysis) observed that of the 14 teams who have <br />
previously played in the championship game (at the end of each season) 5 <br />
have suffered an earlier defeat. "Thus," they conclude, "Ohio State can <br />
still make it to the championship game, but their chances are now less <br />
than 50%."</blockquote><br />
<br />
===Discussion===<br />
<br />
What is wrong with this?<br />
----<br />
Here are forsooths from the September 2005 issues of RSS NEWS<br />
<br />
<blockquote>'Big ticket quiz' at the start of Wimbledon:<br><br><br />
Q. How many punnets (a small light basket or other container for fruit or vegetables) of strawberries are eaten each day during the Wimbledon tournament?<br><br />
Is it (a) over 8,000, (b) over 9,000 or (c) over 10,000?</blockquote><br />
<br />
<div align="right">BBC radio 5<br><br />
20 June 2005</div><br />
<br />
<blockquote>Waiting time for foot surgery down by 500%</blockquote><br />
<br />
<div align="right">Evening News (Edinburgh)<br><br />
5 July 2005</div><br />
<br />
The next two forsooths are from the October RSS news.<br />
<br />
<blockquote>In 1996-8 when the number attending university was static, the participation of women was also static, but male participation fell.</blockquote><br />
<br />
<div align="right">The Times Higher<br><br />
21 January 2005</div><br />
<br />
<blockquote>[On the subject of congestion on the London Underground..] 'Last year 976 million of us used the tube...'</blockquote><br />
<br />
<div align="right">BBC London News<br><br />
19 May 2005</div><br />
<br />
<br />
==Fortune's Formula==<br />
<br />
''Fortune's Formula: Wanna Bet?''<br><br />
''New York Times Book Section'', September 25, 2005<br><br />
David Pogue<br />
<br />
This must be the kind of review that every Science writer dreams of. Pogue ends his review with:<br />
<br />
<blockquote> ''Fortune's Formula'' may be the world's first history book, gambling primer, mathematics text, economics manual, personal finance guide and joke book in a single volume. Poundstone comes across like the best college professor you ever had, someone who can turn almost any technical topic into an entertaining and zesty lecture. But every now and then, you can't help wishing there were some teaching assistants on hand to help.</blockquote><br />
<br />
The author William Poundstone is a science writer who has written a number of very successful science books. His book, ''Prisoner's dilemma: John von Neumann, game theory and the puzzle of the bomb'', was written in the style of this book. Indeed Helen Joyce, in her review of this book in Plus Magazine writes:<br />
<br />
<blockquote>This book is a curious mixture of biography, history and mathematics, all neatly packaged into an entertaining and enlightening read. </blockquote><br />
<br />
Poundstone describes himself as a visual artist who does books as a "day job.". You can learn about his art work [http://www.uiowa.edu/~iareview/tirweb/feature/poundstone/interview2.htm here].<br />
<br />
''Fortune's Formula'' is primarily the story of Edward Thorp, Claude Shannon, and John Kelly and their attempt to use mathematics to make money gambling in casinos and on the stock market. None of these did their graduate work in mathematics. Thorp and Kelly got their Phd's in physics and Shannon in Genetics. <br />
<br />
In the spring of 1955, while a graduate student at UCLA, Thorp joined a discussion on the possiblity of making money from roulette. Thorp suggested that they could taking advantage of the fact that bets are still accepted for a few second after the croupier releases the ball, and in these seconds, he could estimate what part of the wheel the ball would stop. <br />
<br />
Thorp did not pursue this and in 1959 became an instructor in mathematics at M.I.T. Here he became interested in blackjack and developed his famous card counting method for wining at blackjack. He decided to publish his method in the most prestigious journal he could find and settled on ''Proceedings of the National Academy of Sciences''. For this he needed to have a member of the Academy submit his paper. The only member in the math department was Shannon so he had to persuade him of the importance of his paper. Shannon not only agreed but in the process became fascinated by Thorp's idea for beating roulette. He agreed to help Thorp carry this out. They built a roulette machine in Shannon's basement. It worked fine there in trial runs but not so well in the casino so they did not pursue this method of getting rich. <br />
<br />
Of course Thorp is best known for showing that blackjack is a favorable game and giving a method to exploit this fact. Shannon is best known for his work in information theory. Kelly is known his method for gambling in a favorable game. This plays a central role in Poundstone's book and is probably why Pogue felt that it would help if he had a teaching assistant. Poundstone tries to explain Kelly's work in many different ways but what he really needed to understand it is an example but this required too many formulas for a popular book. So we shall include an example from Chance News 7.09. <br />
<br />
Writing for Motley Fool, 3 April 1997 Mark Brady complained about the inumeracy of the general public and gave a number of examples including this one:<br />
<br />
<blockquote> Fear of uncertainty and innumeracy are synergistic. Most people cannot do the odds. What is a better deal over a year? A 100% safe return with 5 percent interest or a 90 percent safe return with a 20 percent return. For the first deal, your return will be 5% percent. For the second, your return will be 8%. Say you invest $1000 10 times. Your interest for the 9 successful deals will be 9000 x 0.2 or 1800. Subtract the 1000 you lost on the 10th deal and you get a $800 return on your original $10,000 for 8 percent.</blockquote><br />
<br />
Peter Doyle suggested that a better investment strategy in this case is:<br />
<br />
Faced with a 100 percent-safe investment returning 5 percent and a 90 percent-safe investment returning 20%, you should invest 20% of your funds in the risky investment and 80% in the safe investment. This gives you an effective return of roughly 5.31962607969968292 percent. <br />
<br />
Peter is using a money management system due to J. L. Kelly (1956: "A new interpretation of information rate," ''Bell System Technical Journal'', '''35'''). Kelly was interested in finding a rational way to invest your money faced with one or more investment schemes, each of which has a positive expected gain. He did not think it reasonable to try simply to maximize your expected return. If you did this in the Motley Fools example as suggested by Mark Brady, you would choose the risky investment and might well lose all your money the first year. We will illustrate what Kelly did propose in terms of Motley Fools example. <br />
<br />
We start with an initial capital, which we choose for convenience to be $1, and invest a fraction r of this money in the gamble and a fraction 1-r in the sure-thing. Then for the next year we use the same fractions to invest the money that resulted from the first year's investments and continue, using the same r each year. Assume, for example, that in the first and third years we win the gamble and in the second year we lose it. Then after 3 years our investment returns an amount f(r) where: <br />
<br />
<math><br />
f(r) = (1.2r + 1.05(1-r))(1.05(1-r))(1.2r + 1.05(1-r)). <br />
</math><br />
<br />
After n years, we would have n such factors, each corresponding to a win or a loss of our risky investment. Since the order of the terms does not matter our capital will be: <br />
<br />
<math><br />
f(r,n) = (1.2r + 1.05(1-r))^W(1.05(1-r))^L<br />
</math><br />
<br />
where W is the number of times we won the risky investment and L the number of times we lost it. Now Kelly calls the quantity:<br />
<br />
<math><br />
G(r) =\lim_{n \to \infty }\frac{\log(f( r,n)} {n}<br />
</math> <br />
<br />
the exponential rate of growth of our capital. In terms of G(r) our capital should grow like <math> e^{G(r)} </math>. In our example: <br />
<br />
<math><br />
\log(\frac{f(r,n)}{n}) = \frac{W}{n}\log(1.2r + 1.05(1-r)) + \frac{L}{n}\log(1.05(1-r))<br />
</math> <br />
<br />
Since we have a 90% chance of winning our gamble, the [http://en.wikipedia.org/wiki/Strong_law_of_large_numbers#The_strong_law strong law of large numbers] tells us that as n tends to infinity this will converge to <br />
<br />
<math><br />
G(r) = 0.9\log(1.2r + 1.05(1-r))+0.1\log(1.05(1-r))<br />
</math><br />
<br />
It is a simple calculus problem to show that G(r) is maximized by r = 0.2 with: <br />
G(0.2) = 0.05183. Then e^{0.05183} = 1.0532, showing that our maximum rate of growth is 5.32% as claimed by Peter. <br />
<br />
The attractiveness of the Kelly investment scheme is that, in the long run, any other investment strategy (including those where you are allowed to change your investment proportions at different times) will do less well. "In the long run and less well" means more precisely that the ratio of your return under the Kelly scheme and your return under any other strategy will tend to infinity.<br />
<br />
Thorp had a very good experience in the stock market, which is described very well by Gaeton Lion in his excellent [http://www.amazon.com/gp/product/customer-reviews/0809046377/ref=cm_cr_dp_pt/103-8647004-5865443?%5Fencoding=UTF8&n=283155&s=books review] of ''Fortune's Formula''. He writes:<br />
<br />
<blockquote> Ed Thorp succeeded in deriving superior returns in both gambling and investing. But, it was not so much because of Kelly's formula. He developed other tools to achieve superior returns. In gambling, Ed Thorp succeeded at Black Jack by developing the card counting method. He just used intuitively Kelly's formula to increase his bets whenever the odds were in his favor. Later, he ran a hedge fund for 20 years until the late 80s and earned a rate of return of 14% handily beating the market's 8% during the period. <br><br><br />
<br />
Also, his hedge fund hardly lost any value on black Monday in October 1987, when the market crashed by 22%. The volatility of his returns was far lower than the market. He did this by exploiting market inefficiencies using warrants, options, and convertible bonds. The Kelly formula was for him a risk management discipline and not a direct source of excess return. </blockquote><br />
<br />
Shannon also made a lot of money on the stock market, but did not use Kelly's formula. In his [http://www.amazon.com/gp/product/customer-reviews/0809046377/ref=cm_cr_dp_pt/103-8647004-5865443?%5Fencoding=UTF8&n=283155&s=books review] Gaeton Lion writes<br />
<br />
<blockquote>Claude Shannon amassed large wealth by recording one of the best investment records. His performance had little to do with Kelly's formula. Between 1966 and 1986, his record beat even Warren Buffet (28% to 27% respectively). Shannon strategy was similar to Buffet. Both their stock portfolios were concentrated, and held for the long term. Shannon achieved his record by holding mainly three stocks (Teledyne, Motorola, and HP). The difference between the two was that Shannon invested in technology because he understood it well, while Buffet did not. </blockquote><br />
<br />
Finally, Thorp provided the following comments for the book cover:<br />
<br />
<blockquote>From bookies to billionaires, you'll meet a motley cast of characters in this highly original, 'outside the box' look at gambling and investing. Read it for the stories alone, and you'll be surprised at how much else you can learn without even trying. --Edward O. Thorp, author of ''Beat the Dealer'' and ''Beat the Market''.</blockquote><br />
<br />
Submitted by Laurie Snell.<br />
<br />
<br />
==Which foods prevent cancer?==<br />
<br />
Which of these foods will stop cancer? (Not so fast)<br><br />
New York Times, 27 September 2005, Sect. F, p. 1<Br><br />
Gina Kolata<br />
<br />
Among other examples, the article includes a [http://www.nytimes.com/imagepages/2005/09/26/science/20050927_CANCER_GRAPHIC.html data graphic] on purported benefits of dietary fiber in preventing colorectal cancer. Early observational studies indicated an association, but subsequent randomized experiments found no effect. <br />
<br />
More to follow.<br />
<br />
<br />
==Slices of risk and the <em>broken heart</em> concept==<br />
[http://www.gloriamundi.org/picsresources/news20050912.pdf How a Formula Ignited Market That Burned Some Big Investors],<br />
Mark Whitehouse, The Wall Street Journal, September 12, 2005.<br><br />
<br />
This on-line article relates how a statistician, David Li,<br />
unknown outside a small coterie of finance theorists, helped change the world of investing. <br />
<br />
The article focuses on a event last May when General Motors Corp's debt<br />
was downgraded to junk status, causing turmoil in some financial markets.<br />
The article gives a nice summary of the underlying financial instruments known<br />
as credit derivatives -<br />
investment contracts structured so their value depends on the behavior of some other thing or event -<br />
with exotic names like <br />
[http://en.wikipedia.org/wiki/Collateralized_debt_obligations collateralized debt obligations] and [http://en.wikipedia.org/wiki/Credit_default_swap credit-default swaps].<br />
<br />
The critical step is to estimate the likelihood that many of the companies <br />
in a pool of companies would go bust at once. <br />
For instance, if the companies were all in closely related industries,<br />
such as auto-parts suppliers, they might fall like dominoes after a catastrophic event.<br />
Such a pool would have a 'high default correlation'.<br />
<br />
In 1997, nobody knew how to calculate default correlations with any precision. <br />
Mr. Li's solution drew inspiration from a concept in actuarial science known as the <br />
<em>broken heart</em> syndrome - people tend to die faster after the death of a beloved spouse. <br />
Some of his colleagues from academia were working on a way to predict this<br />
death correlation, something quite useful to companies that sell life insurance and joint annuities.<br />
He says:<br />
<blockquote><br />
Suddenly I thought that the problem I was trying to solve was exactly like the problem these<br />
guys were trying to solve,.<br />
Default is like the death of a company, so we should<br />
model this the same way we model human life."<br />
</blockquote><br />
<br />
This gave him the idea of using [http://en.wikipedia.org/wiki/Copula_%28statistics%29 copulas], <br />
mathematical functions the colleagues had begun applying to actuarial science. <br />
Copulas help predict the likelihood of various events<br />
occurring when those events depend to some extent on one another. <br />
Until the events last May of this year, one of the most popular copulas for bond pools <br />
was the Gaussian copula, named after <br />
[http://en.wikipedia.org/wiki/Carl_Friedrich_Gauss Carl Friedrich Gauss], a 19th-century German statistician. <br />
<br />
===Further reading===<br />
* The [http://www.gloriamundi.org/picsresources/news20050912.pdf on-line article] gives more details about what went wrong in the financial markets in May and the search for a more appropriate copula to capture better the <em>broken heart</em> syndrome between companies.<br />
* [http://en.wikipedia.org/wiki/Wikipedia Wikipedia] is a very worthwhile on-line resource for definitions of technical words, such as [http://en.wikipedia.org/wiki/Copula_%28statistics%29 copula].<br />
<br />
Submitted by John Gavin.<br />
<br />
<br />
==Learning to speak via statistics and graph theory==<br />
<br />
[http://education.guardian.co.uk/tefl/teaching/story/0,15085,1576100,00.html Computer learns grammar by crunching sentences], Max de Lotbinière September 23, 2005, [http://www.guardianweekly.co.uk/ Guardian Weekly].<br><br />
[http://www.cornellsun.com/vnews/display.v/ART/2005/09/09/432118a84f6af Profs’ New Software ‘Learns’ Languages], Ben Birnbaum, 9 Sep 2005, Cornell Daily Sun.<br />
<br />
A language-learning robot may sound like science fiction but new software, developed by Cornell University psychology professor Shimon Edelman, with colleagues Zach Solan, David Horn and Eytan Ruppin from Tel Aviv University in Israel, is well on the way to constructing a computer program that can teach itself languages and make up its own sentences, the developers' claim.<br />
<br />
Unlike previous attempts at developing computer algorithms for language learning - "Automatic Distillation of Structure," or "ADIOS" for short - discovers complex patterns in raw text by repeatedly aligning sentences and looking for overlapping parts.<br />
Once it has derived a language's rules of grammar,<br />
it can then produce sentences of its own, simply from blocks of text in that language.<br />
<br />
It has been evaluated on artificial context-free grammars with thousands of rules, <br />
on natural languages as diverse as English and Chinese, <br />
on coding regions in DNA sequences and on protein data correlating sequence with function. <br />
<br />
Edelman comments:<br />
<blockquote><br />
Adios relies on a statistical method for pattern extraction and on structured generalisations <br />
- the two processes that have been implicated in language acquisition.<br />
Our experiments show that Adios can acquire intricate structures <br />
from raw data including transcripts of parents' speech directed at two- or three-year-olds.<br />
This may eventually help researchers understand how children, <br />
who learn language in a similar item-by-item fashion, and with little supervision, <br />
eventually master the full complexity of their native tongue.<br />
</blockquote><br />
<br />
[http://plus.maths.org/latestnews/may-aug05/adios/ Plus Magazine's website]<br />
offers a more logical explanation:<br />
<blockquote><br />
The ADIOS algorithm is based on statistical and algebraic methods performed on one of the most basic and versatile objects of mathematics - the graph.<br />
Given a text, the program loads it as a graph by representing each word by a node, or vertex, and each sentence by a sequence of nodes connected by lines. A string of words in the text is now represented by a path in the graph. <br><br />
<br />
Next it performs a statistical analysis to see which paths, or strings of words, occur unusually often. <br />
It then decides that those that appear most frequently - called "significant patterns" - <br />
can safely be regarded as a single unit<br />
and replaces the set of vertices in each of these patterns by a single vertex, <br />
thus creating a new, generalised, graph.<br><br />
<br />
Finally, the program looks for paths in the graph which just differ by one vertex. <br />
These stand for parts of sentences that just differ by one word (or compound of words) like "the cat is hungry" and "the dog is hungry". <br />
Performing another statistical test on the frequency of these paths, the program identifies classes of vertices, or words, that can be regarded as interchangeable, or equivalent. <br />
The sentence involved is legitimate no matter which of the words in the class - in our example "cat" or "dog" - you put in.<br><br />
<br />
This last step is then repeated recursively.<br><br />
</blockquote><br />
<br />
[http://plus.maths.org/latestnews/may-aug05/adios/ The website] uses graphs to illustrate some examples and it finishes with some reassuring words:<br />
<blockquote><br />
All this doesn't mean, of course, that the program actually "understands" what it's saying. It simply knows how to have a good go at piecing together fragments of sentences it has identified, in the hope that they are grammatically correct. So if, like me, you're prone to swearing at your computer, you can safely continue to do so: it won't answer back for a long while yet.<br />
</blockquote><br />
<br />
===Further reading===<br />
The [http://adios.tau.ac.il/ ADIOS homepage] offers an overview and more detailed description of the program.<br />
<br />
Submitted by John Gavin.<br />
<br />
==Understanding probability==<br />
<br />
Understanding Probability:Chance rules in everyday life<br><br />
Cambridge University Press 2004<br><br />
Henk Tijms<br />
<br />
Hank Tijms is Professor in Operation Research at the Vrije University in Amsterdam. This book is based on his earlier Dutch book “Spelen met Kansen.” <br />
<br />
The aim of this book is to show how probability applies to our everyday life in a way that your Uncle George could understand even if he has forgotten much of his high school math. Tijms does not try to avoid mathematics but only to postpone the formal math until the reader has seen the many applications of probability in the real world, how much fun it is, and learned to work problems and when he can’t work one how to get the answer by simulation. He learns all this in part I of the book and then he learns the more formal math in Part II.<br />
<br />
In Chapter 1 Tijms asks the reader to think about problems with surprising answers in the spirit of Susan Holmes “[http://www-stat.stanford.edu/~susan/surprise/ Probability by Surprise]” including the birthday problem and the Monty Hall problem. Readers are on their own to try to solve one or more of the problems but promised that they will see the solutions later in the book. <br />
<br />
Chapter 2 deals with the law of large numbers and introduces the concept of simulation. This theorem is explained and illustrated by problems related, for example, to coin tossing, random walks and casino games. Expected value is introduced in an informal way to be defined more carefully later in the book. For the reader who is not frightened by mathematical formulas, Tijms includes a discussion of the Kelly betting system with a footnote saying that this paragraph can be skipped at first reading. This is a fascinating topic that is widely applied in gambling and stock investment but rarely appears in a probability book.<br />
<br />
In Chapter 3 the author returns to previous problems such as the birthday problem and gambling systems and solves them first by simulation and then by mathematics. <br />
<br />
In this chapter Tijms describes Efron’s bootstrap method and uses it to solve a number of problems including a hypothetical clinical trial and to test if the famous 1970 draft lottery during the Vietnam War was fair. Again the bootstrap method has wide application but rarely occurs in an elementary probability or statistics book.<br />
<br />
Chapter 4 describes the binomial, Poisson, and hypergeomtric distributions and how to use them in solving problems such as the famous hat check problem, and a variety of interesting lottery questions. The Poisson process is discussed but again with the footnote that novice readers might want to read this at a later time.<br />
<br />
Chapter 5 is mainly about Center Limit Theorem and its many applications especially to statistics. <br />
<br />
Chapter 6 introduces Chance trees and Bayes’s rule. The tree method is used to explain a variety of problems including the Monty Hall Problem and the false-positive paradox. <br />
<br />
This is a brief description of the first six chapters which constitute Part I of the book. Now the fun is over. Part 2 called “Essentials of probability” looks like the traditional first chapters in a standard probability book. But the reader has already found how exciting probability is, has a good intuitive idea of the basic concepts and has worked many of the interesting problems at the end of each chapter either using math or simulation. For some students this might allow them to actually enjoy Part 2. But your Uncle George may want to quit while they are ahead. <br />
<br />
Tijms writes with great clarity and his enthusiasm for probability in the real world is contagious. We were delighted to see, as acknowledged in the preface, that Tijms included several of the more interesting problems discussed in Chance News, often going well beyond what we had said in our discussion of the problem. <br />
<br />
This book presents a completely new way to go about teaching a first course in probability and we think those who teach such a course should consider trying it out.<br />
<br />
===Discussion===<br />
<br />
(1) In the days of Basic we required all students to learn Basic in their first math course so we could assume that students could write programs to simulate probability problems and so me made heavy use of simulation as suggested in this book. The author uses Pascal in his book. What present language do you think is easiest for a student with no computing experience to learn?<br />
<br />
We asked Professor Tijms what the situation was in math departments in Europe and he replied:<br />
<br />
<blockquote>In math departments of universities and polytechnic schools in Europe students learn to write computer programs. In my university they still learn to program in Java and C++ ( in previous days Pascal), but I see in the Netherlands the trend that the instructors think it is sufficient if the students are able to program in Matlab. <br><br><br />
<br />
In ny book I have chosen to formulate the simulation programs in Pascal because of the clarity and the simplicity of the language, though this language is hardly used anymore. The introductory probability course at my university is given before they have learned to program, but this does not prevent them of simulating probability problems by using Excel. In the simulation of many elementary probability problems a random-number generator alone suffices to simulate those problems and so Excel can be used. In the second year they have mastered Matlab, a perfect tool with its excellent graphics to simulate many challenging probability problems ( they really like it, in particular when it concerns problems such as the problems 2.24-2.45 in chapter 2 and the problems 5.11-5.13 in chapter 5). <br />
</blockquote><br />
<br />
<br />
(2) Do you think that probability books should include data to test probability models that are said to describe real world problems? If so name some models that you think would pass such a test and some that you think might not.<br />
<br />
Submitted by Laurie Snell<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Societies worse off when they have God on their side==<br />
<br />
[http://www.timesonline.co.uk/article/0,,2-1798944,00.html Societies worse off when they have God on their side]<br><br />
Timesonline, September 27, 2005<br><br />
Ruth Gledhill<br />
<br />
[http://moses.creighton.edu/JRS/2005/2005-11.html Cross-national correlations of quantifiable societal health with popular religiosity and secularism in the prosperous democracies]<br><br />
Journal of Religion & Society, Vol.7(2005)<br><br />
Gregory S. Paul<br />
<br />
In the Times article we read:<br />
<br />
<blockquote>According to the study, belief in and worship of God are not only unnecessary for a healthy society but may actually contribute to social problems.<br><br><br />
Many liberal Christians and believers of other faiths hold that religious belief is socially beneficial, believing that it helps to lower rates of violent crime, murder, suicide, sexual promiscuity and abortion. The benefits of religious belief to a society have been described as its “spiritual capital”. But the study claims that the devotion of many in the US may actually contribute to its ills. <br />
</blockquote><br />
<br />
Gregory Paul is a dinosaur paleontologist and on an [http://www.abc.net.au/worldtoday/indexes/2005/twt_20050928.htm interview] on Australian ABC radio Paul said that, being a paleontologist, for many years he had to deal with the issue of creationism versus evolutionary science in the U.S and his interest in evolutionary science prompted him to look at whether there was any link between the religiosity of a society and how well that society functions. <br />
<br />
If you look at Paul's article you will find very little technical statistical analysis, for example, he did not carry out a regression analysis. Rather he rests his case on the series of scatterplots.<br />
<br />
Paul describes his data sources as:<br />
<br />
<blockquote>Data sources for rates of religious belief and practice as well as acceptance of evolution are the 1993 Environment I (Bishop) and 1998 Religion II polls conducted by the International Social Survey Program (ISSP), a cross-national collaboration on social science surveys using standard methodologies that currently involves 38 nations. The last survey interviewed approximately 23,000 people in almost all (17) of the developed democracies; Portugal is also plotted as an example of a second world European democracy. Results for western and eastern Germany are combined following the regions' populations. England is generally Great Britain excluding Northern Ireland; Holland is all of the Netherlands. The results largely agree with national surveys on the same subjects; for example, both ISSP and Gallup indicate that absolute plus less certain believers in a higher power are about 90% of the U.S. population. The plots include Bible literalism and frequency of prayer and service attendance, as well as absolute belief in a creator, in order to examine religiosity in terms of ardency, conservatism, and activities. </blockquote><br />
<br />
Here are the countries Paul considered with the abbreviations used on the graphics. <br />
<br />
A = Australia, C = Canada, D = Denmark, E = Great Britain, F = France, G = Germany,<br />
H = Holland, I = Ireland, J = Japan, L = Switzerland, N = Norway, P = Portugal, R = Austria,<br />
S = Spain, T = Italy, U = United States, W = Sweden, Z = New Zealand.<br />
<br />
There seems to be no agreement as to which countries are developed democracies. For example Paul might have included Greece and Belgium, Finland, and others but the data may have determined his choice. Paul comments that he added Portugal as an example of a second world democracy. <br />
<br />
Paul's anaysis of the data includes a series of 9 Figures which are available at the end of the article and are the most interesting part of the study. If you try printing Paul's article you will only get the first of his 9 Figures. When you look at the [http://moses.creighton.edu/JRS/2005/2005-11.html web version] you will still see only Figure 1 but the others can be viewed by selecting the numbers from 2 to 9 on the left side of Figure 1.<br />
<br />
Figure 1 deals with the proportion of people who accept human evolution which is interesting but not as relevant to the welfare of the people as others so we will look at Figure 2.<br />
<br />
[[Image:religion2.png|500px|center|Source:Gregory Paul]]<br />
<br />
Each Figure iprovides 5 separate scatterplots. Ïn Figure 2 we see that the U.S. has largest number--between 6 and 7-- of homicides per 100,000 and Spain has the lowest number with less than 1 homicide per 100,000. We also see that the U.S. has the highest proportion of people, about 25%, who take the bible literally while several countries have less than 10% such people.<br />
<br />
What we cannot do is compare the number of homicides per thousand between those who take the bible literally and those who are agnostics or atheists which is what we would really want to know. Presumably the data did not permit this comparison. <br />
<br />
[[Image:religion3.png|500px|center|Source:Gregory Paul]]<br />
<br />
Figure 3 deals with "14-24 year old suicides per 100,000". Here the U.S. is in about the middle.<br />
<br />
Figure 4 deals with the "under-five mortalities per 1000 births".<br />
<br />
[[Image:religion4.png|500px|center|Source:Gregory Paul]]<br />
<br />
Ignoring Portugal, the U.S. has the highest number of under-five mortalities per 1000 births-- between 7 and--8 while several countries have only 4.<br />
<br />
The other figures can be seen at end of Paul's article. They deal with life expectancy, sexually transmitted diseases, abortion and 15-16 year old pregnancies. Life expectancy is the smallest in the U.S. and for sexually transmitted diseases, abortion and 15-17 year old prenacies the U.S. is at the top of the graphs and in fact these look like outliers.<br />
<br />
Well, this study does not by itself justify the Times hedline: "Societies worse off when they have God on their side." Paul himself would not claim this. He writes:<br />
<br />
<blockquote> This study is a first, brief look at an important subject that has been almost entirely neglected by social scientists. The primary intent is to present basic correlations of the elemental data. Some conclusions that can be gleaned from the plots are outlined. This is not an attempt to present a definitive study that establishes cause versus effect between religiosity, secularism and societal health. It is hoped that these original correlations and results will spark future research and debate on the issue.</block<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div></div>Nano12https://www.causeweb.org/wiki/chance/index.php?title=Chance_News_7&diff=1536Chance News 72005-11-05T09:33:07Z<p>Nano12: /* Understanding probability */</p>
<hr />
<div>Sept 26 2005 to Oct 15 2005<br />
==Quotation==<br />
<blockquote><br />
While writing my book [Stochastic Processes] I had an argument with Feller [Introuction to Probability Theory and its Applications]. He asserted that everyone said "random variable" and I asserted that everyone said "chance variable." We obviously had to use the same name in our books, so we decided the issue by a stochastic procedure. That is, we tossed for it and he won. </blockquote><br />
<br />
<p align = right> Joe Doob<br><br />
[http://www.dartmouth.edu/~chance/Doob/conversation.html Statistical Science]<br><br />
<br />
==Forsooth==<br />
<br />
Peter Winkler suggested our first forsooth.<br />
<br />
<blockquote>Texas beats Ohio State in their opening game <br />
of the season (Saturday Sept 10 2002). The sportscasters (legendary Brent Musburger on play-by-play or Gary Danielson on analysis) observed that of the 14 teams who have <br />
previously played in the championship game (at the end of each season) 5 <br />
have suffered an earlier defeat. "Thus," they conclude, "Ohio State can <br />
still make it to the championship game, but their chances are now less <br />
than 50%."</blockquote><br />
<br />
===Discussion===<br />
<br />
What is wrong with this?<br />
----<br />
Here are forsooths from the September 2005 issues of RSS NEWS<br />
<br />
<blockquote>'Big ticket quiz' at the start of Wimbledon:<br><br><br />
Q. How many punnets (a small light basket or other container for fruit or vegetables) of strawberries are eaten each day during the Wimbledon tournament?<br><br />
Is it (a) over 8,000, (b) over 9,000 or (c) over 10,000?</blockquote><br />
<br />
<div align="right">BBC radio 5<br><br />
20 June 2005</div><br />
<br />
<blockquote>Waiting time for foot surgery down by 500%</blockquote><br />
<br />
<div align="right">Evening News (Edinburgh)<br><br />
5 July 2005</div><br />
<br />
The next two forsooths are from the October RSS news.<br />
<br />
<blockquote>In 1996-8 when the number attending university was static, the participation of women was also static, but male participation fell.</blockquote><br />
<br />
<div align="right">The Times Higher<br><br />
21 January 2005</div><br />
<br />
<blockquote>[On the subject of congestion on the London Underground..] 'Last year 976 million of us used the tube...'</blockquote><br />
<br />
<div align="right">BBC London News<br><br />
19 May 2005</div><br />
<br />
<br />
==Fortune's Formula==<br />
<br />
''Fortune's Formula: Wanna Bet?''<br><br />
''New York Times Book Section'', September 25, 2005<br><br />
David Pogue<br />
<br />
This must be the kind of review that every Science writer dreams of. Pogue ends his review with:<br />
<br />
<blockquote> ''Fortune's Formula'' may be the world's first history book, gambling primer, mathematics text, economics manual, personal finance guide and joke book in a single volume. Poundstone comes across like the best college professor you ever had, someone who can turn almost any technical topic into an entertaining and zesty lecture. But every now and then, you can't help wishing there were some teaching assistants on hand to help.</blockquote><br />
<br />
The author William Poundstone is a science writer who has written a number of very successful science books. His book, ''Prisoner's dilemma: John von Neumann, game theory and the puzzle of the bomb'', was written in the style of this book. Indeed Helen Joyce, in her review of this book in Plus Magazine writes:<br />
<br />
<blockquote>This book is a curious mixture of biography, history and mathematics, all neatly packaged into an entertaining and enlightening read. </blockquote><br />
<br />
Poundstone describes himself as a visual artist who does books as a "day job.". You can learn about his art work [http://www.uiowa.edu/~iareview/tirweb/feature/poundstone/interview2.htm here].<br />
<br />
''Fortune's Formula'' is primarily the story of Edward Thorp, Claude Shannon, and John Kelly and their attempt to use mathematics to make money gambling in casinos and on the stock market. None of these did their graduate work in mathematics. Thorp and Kelly got their Phd's in physics and Shannon in Genetics. <br />
<br />
In the spring of 1955, while a graduate student at UCLA, Thorp joined a discussion on the possiblity of making money from roulette. Thorp suggested that they could taking advantage of the fact that bets are still accepted for a few second after the croupier releases the ball, and in these seconds, he could estimate what part of the wheel the ball would stop. <br />
<br />
Thorp did not pursue this and in 1959 became an instructor in mathematics at M.I.T. Here he became interested in blackjack and developed his famous card counting method for wining at blackjack. He decided to publish his method in the most prestigious journal he could find and settled on ''Proceedings of the National Academy of Sciences''. For this he needed to have a member of the Academy submit his paper. The only member in the math department was Shannon so he had to persuade him of the importance of his paper. Shannon not only agreed but in the process became fascinated by Thorp's idea for beating roulette. He agreed to help Thorp carry this out. They built a roulette machine in Shannon's basement. It worked fine there in trial runs but not so well in the casino so they did not pursue this method of getting rich. <br />
<br />
Of course Thorp is best known for showing that blackjack is a favorable game and giving a method to exploit this fact. Shannon is best known for his work in information theory. Kelly is known his method for gambling in a favorable game. This plays a central role in Poundstone's book and is probably why Pogue felt that it would help if he had a teaching assistant. Poundstone tries to explain Kelly's work in many different ways but what he really needed to understand it is an example but this required too many formulas for a popular book. So we shall include an example from Chance News 7.09. <br />
<br />
Writing for Motley Fool, 3 April 1997 Mark Brady complained about the inumeracy of the general public and gave a number of examples including this one:<br />
<br />
<blockquote> Fear of uncertainty and innumeracy are synergistic. Most people cannot do the odds. What is a better deal over a year? A 100% safe return with 5 percent interest or a 90 percent safe return with a 20 percent return. For the first deal, your return will be 5% percent. For the second, your return will be 8%. Say you invest $1000 10 times. Your interest for the 9 successful deals will be 9000 x 0.2 or 1800. Subtract the 1000 you lost on the 10th deal and you get a $800 return on your original $10,000 for 8 percent.</blockquote><br />
<br />
Peter Doyle suggested that a better investment strategy in this case is:<br />
<br />
Faced with a 100 percent-safe investment returning 5 percent and a 90 percent-safe investment returning 20%, you should invest 20% of your funds in the risky investment and 80% in the safe investment. This gives you an effective return of roughly 5.31962607969968292 percent. <br />
<br />
Peter is using a money management system due to J. L. Kelly (1956: "A new interpretation of information rate," ''Bell System Technical Journal'', '''35'''). Kelly was interested in finding a rational way to invest your money faced with one or more investment schemes, each of which has a positive expected gain. He did not think it reasonable to try simply to maximize your expected return. If you did this in the Motley Fools example as suggested by Mark Brady, you would choose the risky investment and might well lose all your money the first year. We will illustrate what Kelly did propose in terms of Motley Fools example. <br />
<br />
We start with an initial capital, which we choose for convenience to be $1, and invest a fraction r of this money in the gamble and a fraction 1-r in the sure-thing. Then for the next year we use the same fractions to invest the money that resulted from the first year's investments and continue, using the same r each year. Assume, for example, that in the first and third years we win the gamble and in the second year we lose it. Then after 3 years our investment returns an amount f(r) where: <br />
<br />
<math><br />
f(r) = (1.2r + 1.05(1-r))(1.05(1-r))(1.2r + 1.05(1-r)). <br />
</math><br />
<br />
After n years, we would have n such factors, each corresponding to a win or a loss of our risky investment. Since the order of the terms does not matter our capital will be: <br />
<br />
<math><br />
f(r,n) = (1.2r + 1.05(1-r))^W(1.05(1-r))^L<br />
</math><br />
<br />
where W is the number of times we won the risky investment and L the number of times we lost it. Now Kelly calls the quantity:<br />
<br />
<math><br />
G(r) =\lim_{n \to \infty }\frac{\log(f( r,n)} {n}<br />
</math> <br />
<br />
the exponential rate of growth of our capital. In terms of G(r) our capital should grow like <math> e^{G(r)} </math>. In our example: <br />
<br />
<math><br />
\log(\frac{f(r,n)}{n}) = \frac{W}{n}\log(1.2r + 1.05(1-r)) + \frac{L}{n}\log(1.05(1-r))<br />
</math> <br />
<br />
Since we have a 90% chance of winning our gamble, the [http://en.wikipedia.org/wiki/Strong_law_of_large_numbers#The_strong_law strong law of large numbers] tells us that as n tends to infinity this will converge to <br />
<br />
<math><br />
G(r) = 0.9\log(1.2r + 1.05(1-r))+0.1\log(1.05(1-r))<br />
</math><br />
<br />
It is a simple calculus problem to show that G(r) is maximized by r = 0.2 with: <br />
G(0.2) = 0.05183. Then e^{0.05183} = 1.0532, showing that our maximum rate of growth is 5.32% as claimed by Peter. <br />
<br />
The attractiveness of the Kelly investment scheme is that, in the long run, any other investment strategy (including those where you are allowed to change your investment proportions at different times) will do less well. "In the long run and less well" means more precisely that the ratio of your return under the Kelly scheme and your return under any other strategy will tend to infinity.<br />
<br />
Thorp had a very good experience in the stock market, which is described very well by Gaeton Lion in his excellent [http://www.amazon.com/gp/product/customer-reviews/0809046377/ref=cm_cr_dp_pt/103-8647004-5865443?%5Fencoding=UTF8&n=283155&s=books review] of ''Fortune's Formula''. He writes:<br />
<br />
<blockquote> Ed Thorp succeeded in deriving superior returns in both gambling and investing. But, it was not so much because of Kelly's formula. He developed other tools to achieve superior returns. In gambling, Ed Thorp succeeded at Black Jack by developing the card counting method. He just used intuitively Kelly's formula to increase his bets whenever the odds were in his favor. Later, he ran a hedge fund for 20 years until the late 80s and earned a rate of return of 14% handily beating the market's 8% during the period. <br><br><br />
<br />
Also, his hedge fund hardly lost any value on black Monday in October 1987, when the market crashed by 22%. The volatility of his returns was far lower than the market. He did this by exploiting market inefficiencies using warrants, options, and convertible bonds. The Kelly formula was for him a risk management discipline and not a direct source of excess return. </blockquote><br />
<br />
Shannon also made a lot of money on the stock market, but did not use Kelly's formula. In his [http://www.amazon.com/gp/product/customer-reviews/0809046377/ref=cm_cr_dp_pt/103-8647004-5865443?%5Fencoding=UTF8&n=283155&s=books review] Gaeton Lion writes<br />
<br />
<blockquote>Claude Shannon amassed large wealth by recording one of the best investment records. His performance had little to do with Kelly's formula. Between 1966 and 1986, his record beat even Warren Buffet (28% to 27% respectively). Shannon strategy was similar to Buffet. Both their stock portfolios were concentrated, and held for the long term. Shannon achieved his record by holding mainly three stocks (Teledyne, Motorola, and HP). The difference between the two was that Shannon invested in technology because he understood it well, while Buffet did not. </blockquote><br />
<br />
Finally, Thorp provided the following comments for the book cover:<br />
<br />
<blockquote>From bookies to billionaires, you'll meet a motley cast of characters in this highly original, 'outside the box' look at gambling and investing. Read it for the stories alone, and you'll be surprised at how much else you can learn without even trying. --Edward O. Thorp, author of ''Beat the Dealer'' and ''Beat the Market''.</blockquote><br />
<br />
Submitted by Laurie Snell.<br />
<br />
<br />
==Which foods prevent cancer?==<br />
<br />
Which of these foods will stop cancer? (Not so fast)<br><br />
New York Times, 27 September 2005, Sect. F, p. 1<Br><br />
Gina Kolata<br />
<br />
Among other examples, the article includes a [http://www.nytimes.com/imagepages/2005/09/26/science/20050927_CANCER_GRAPHIC.html data graphic] on purported benefits of dietary fiber in preventing colorectal cancer. Early observational studies indicated an association, but subsequent randomized experiments found no effect. <br />
<br />
More to follow.<br />
<br />
<br />
==Slices of risk and the <em>broken heart</em> concept==<br />
[http://www.gloriamundi.org/picsresources/news20050912.pdf How a Formula Ignited Market That Burned Some Big Investors],<br />
Mark Whitehouse, The Wall Street Journal, September 12, 2005.<br><br />
<br />
This on-line article relates how a statistician, David Li,<br />
unknown outside a small coterie of finance theorists, helped change the world of investing. <br />
<br />
The article focuses on a event last May when General Motors Corp's debt<br />
was downgraded to junk status, causing turmoil in some financial markets.<br />
The article gives a nice summary of the underlying financial instruments known<br />
as credit derivatives -<br />
investment contracts structured so their value depends on the behavior of some other thing or event -<br />
with exotic names like <br />
[http://en.wikipedia.org/wiki/Collateralized_debt_obligations collateralized debt obligations] and [http://en.wikipedia.org/wiki/Credit_default_swap credit-default swaps].<br />
<br />
The critical step is to estimate the likelihood that many of the companies <br />
in a pool of companies would go bust at once. <br />
For instance, if the companies were all in closely related industries,<br />
such as auto-parts suppliers, they might fall like dominoes after a catastrophic event.<br />
Such a pool would have a 'high default correlation'.<br />
<br />
In 1997, nobody knew how to calculate default correlations with any precision. <br />
Mr. Li's solution drew inspiration from a concept in actuarial science known as the <br />
<em>broken heart</em> syndrome - people tend to die faster after the death of a beloved spouse. <br />
Some of his colleagues from academia were working on a way to predict this<br />
death correlation, something quite useful to companies that sell life insurance and joint annuities.<br />
He says:<br />
<blockquote><br />
Suddenly I thought that the problem I was trying to solve was exactly like the problem these<br />
guys were trying to solve,.<br />
Default is like the death of a company, so we should<br />
model this the same way we model human life."<br />
</blockquote><br />
<br />
This gave him the idea of using [http://en.wikipedia.org/wiki/Copula_%28statistics%29 copulas], <br />
mathematical functions the colleagues had begun applying to actuarial science. <br />
Copulas help predict the likelihood of various events<br />
occurring when those events depend to some extent on one another. <br />
Until the events last May of this year, one of the most popular copulas for bond pools <br />
was the Gaussian copula, named after <br />
[http://en.wikipedia.org/wiki/Carl_Friedrich_Gauss Carl Friedrich Gauss], a 19th-century German statistician. <br />
<br />
===Further reading===<br />
* The [http://www.gloriamundi.org/picsresources/news20050912.pdf on-line article] gives more details about what went wrong in the financial markets in May and the search for a more appropriate copula to capture better the <em>broken heart</em> syndrome between companies.<br />
* [http://en.wikipedia.org/wiki/Wikipedia Wikipedia] is a very worthwhile on-line resource for definitions of technical words, such as [http://en.wikipedia.org/wiki/Copula_%28statistics%29 copula].<br />
<br />
Submitted by John Gavin.<br />
<br />
<br />
==Learning to speak via statistics and graph theory==<br />
<br />
[http://education.guardian.co.uk/tefl/teaching/story/0,15085,1576100,00.html Computer learns grammar by crunching sentences], Max de Lotbinière September 23, 2005, [http://www.guardianweekly.co.uk/ Guardian Weekly].<br><br />
[http://www.cornellsun.com/vnews/display.v/ART/2005/09/09/432118a84f6af Profs’ New Software ‘Learns’ Languages], Ben Birnbaum, 9 Sep 2005, Cornell Daily Sun.<br />
<br />
A language-learning robot may sound like science fiction but new software, developed by Cornell University psychology professor Shimon Edelman, with colleagues Zach Solan, David Horn and Eytan Ruppin from Tel Aviv University in Israel, is well on the way to constructing a computer program that can teach itself languages and make up its own sentences, the developers' claim.<br />
<br />
Unlike previous attempts at developing computer algorithms for language learning - "Automatic Distillation of Structure," or "ADIOS" for short - discovers complex patterns in raw text by repeatedly aligning sentences and looking for overlapping parts.<br />
Once it has derived a language's rules of grammar,<br />
it can then produce sentences of its own, simply from blocks of text in that language.<br />
<br />
It has been evaluated on artificial context-free grammars with thousands of rules, <br />
on natural languages as diverse as English and Chinese, <br />
on coding regions in DNA sequences and on protein data correlating sequence with function. <br />
<br />
Edelman comments:<br />
<blockquote><br />
Adios relies on a statistical method for pattern extraction and on structured generalisations <br />
- the two processes that have been implicated in language acquisition.<br />
Our experiments show that Adios can acquire intricate structures <br />
from raw data including transcripts of parents' speech directed at two- or three-year-olds.<br />
This may eventually help researchers understand how children, <br />
who learn language in a similar item-by-item fashion, and with little supervision, <br />
eventually master the full complexity of their native tongue.<br />
</blockquote><br />
<br />
[http://plus.maths.org/latestnews/may-aug05/adios/ Plus Magazine's website]<br />
offers a more logical explanation:<br />
<blockquote><br />
The ADIOS algorithm is based on statistical and algebraic methods performed on one of the most basic and versatile objects of mathematics - the graph.<br />
Given a text, the program loads it as a graph by representing each word by a node, or vertex, and each sentence by a sequence of nodes connected by lines. A string of words in the text is now represented by a path in the graph. <br><br />
<br />
Next it performs a statistical analysis to see which paths, or strings of words, occur unusually often. <br />
It then decides that those that appear most frequently - called "significant patterns" - <br />
can safely be regarded as a single unit<br />
and replaces the set of vertices in each of these patterns by a single vertex, <br />
thus creating a new, generalised, graph.<br><br />
<br />
Finally, the program looks for paths in the graph which just differ by one vertex. <br />
These stand for parts of sentences that just differ by one word (or compound of words) like "the cat is hungry" and "the dog is hungry". <br />
Performing another statistical test on the frequency of these paths, the program identifies classes of vertices, or words, that can be regarded as interchangeable, or equivalent. <br />
The sentence involved is legitimate no matter which of the words in the class - in our example "cat" or "dog" - you put in.<br><br />
<br />
This last step is then repeated recursively.<br><br />
</blockquote><br />
<br />
[http://plus.maths.org/latestnews/may-aug05/adios/ The website] uses graphs to illustrate some examples and it finishes with some reassuring words:<br />
<blockquote><br />
All this doesn't mean, of course, that the program actually "understands" what it's saying. It simply knows how to have a good go at piecing together fragments of sentences it has identified, in the hope that they are grammatically correct. So if, like me, you're prone to swearing at your computer, you can safely continue to do so: it won't answer back for a long while yet.<br />
</blockquote><br />
<br />
===Further reading===<br />
The [http://adios.tau.ac.il/ ADIOS homepage] offers an overview and more detailed description of the program.<br />
<br />
Submitted by John Gavin.<br />
<br />
==Understanding probability==<br />
<br />
Understanding Probability:Chance rules in everyday life<br><br />
Cambridge University Press 2004<br><br />
Henk Tijms<br />
<br />
Hank Tijms is Professor in Operation Research at the Vrije University in Amsterdam. This book is based on his earlier Dutch book “Spelen met Kansen.” <br />
<br />
The aim of this book is to show how probability applies to our everyday life in a way that your Uncle George could understand even if he has forgotten much of his high school math. Tijms does not try to avoid mathematics but only to postpone the formal math until the reader has seen the many applications of probability in the real world, how much fun it is, and learned to work problems and when he can’t work one how to get the answer by simulation. He learns all this in part I of the book and then he learns the more formal math in Part II.<br />
<br />
In Chapter 1 Tijms asks the reader to think about problems with surprising answers in the spirit of Susan Holmes “[http://www-stat.stanford.edu/~susan/surprise/ Probability by Surprise]” including the birthday problem and the Monty Hall problem. Readers are on their own to try to solve one or more of the problems but promised that they will see the solutions later in the book. <br />
<br />
Chapter 2 deals with the law of large numbers and introduces the concept of simulation. This theorem is explained and illustrated by problems related, for example, to coin tossing, random walks and casino games. Expected value is introduced in an informal way to be defined more carefully later in the book. For the reader who is not frightened by mathematical formulas, Tijms includes a discussion of the Kelly betting system with a footnote saying that this paragraph can be skipped at first reading. This is a fascinating topic that is widely applied in gambling and stock investment but rarely appears in a probability book.<br />
<br />
In Chapter 3 the author returns to previous problems such as the birthday problem and gambling systems and solves them first by simulation and then by mathematics. <br />
<br />
In this chapter Tijms describes Efron’s bootstrap method and uses it to solve a number of problems including a hypothetical clinical trial and to test if the famous 1970 draft lottery during the Vietnam War was fair. Again the bootstrap method has wide application but rarely occurs in an elementary probability or statistics book.<br />
<br />
Chapter 4 describes the binomial, Poisson, and hypergeomtric distributions and how to use them in solving problems such as the famous hat check problem, and a variety of interesting lottery questions. The Poisson process is discussed but again with the footnote that novice readers might want to read this at a later time.<br />
<br />
Chapter 5 is mainly about Center Limit Theorem and its many applications especially to statistics. <br />
<br />
Chapter 6 introduces Chance trees and Bayes’s rule. The tree method is used to explain a variety of problems including the Monty Hall Problem and the false-positive paradox. <br />
<br />
This is a brief description of the first six chapters which constitute Part I of the book. Now the fun is over. Part 2 called “Essentials of probability” looks like the traditional first chapters in a standard probability book. But the reader has already found how exciting probability is, has a good intuitive idea of the basic concepts and has worked many of the interesting problems at the end of each chapter either using math or simulation. For some students this might allow them to actually enjoy Part 2. But your Uncle George may want to quit while they are ahead. <br />
<br />
Tijms writes with great clarity and his enthusiasm for probability in the real world is contagious. We were delighted to see, as acknowledged in the preface, that Tijms included several of the more interesting problems discussed in Chance News, often going well beyond what we had said in our discussion of the problem. <br />
<br />
This book presents a completely new way to go about teaching a first course in probability and we think those who teach such a course should consider trying it out.<br />
<br />
===Discussion===<br />
<br />
(1) In the days of Basic we required all students to learn Basic in their first math course so we could assume that students could write programs to simulate probability problems and so me made heavy use of simulation as suggested in this book. The author uses Pascal in his book. What present language do you think is easiest for a student with no computing experience to learn?<br />
<br />
We asked Professor Tijms what the situation was in math departments in Europe and he replied:<br />
<br />
<blockquote>In math departments of universities and polytechnic schools in Europe students learn to write computer programs. In my university they still learn to program in Java and C++ ( in previous days Pascal), but I see in the Netherlands the trend that the instructors think it is sufficient if the students are able to program in Matlab. <br><br><br />
<br />
In ny book I have chosen to formulate the simulation programs in Pascal because of the clarity and the simplicity of the language, though this language is hardly used anymore. The introductory probability course at my university is given before they have learned to program, but this does not prevent them of simulating probability problems by using Excel. In the simulation of many elementary probability problems a random-number generator alone suffices to simulate those problems and so Excel can be used. In the second year they have mastered Matlab, a perfect tool with its excellent graphics to simulate many challenging probability problems ( they really like it, in particular when it concerns problems such as the problems 2.24-2.45 in chapter 2 and the problems 5.11-5.13 in chapter 5). <br />
</blockquote><br />
<br />
<br />
(2) Do you think that probability books should include data to test probability models that are said to describe real world problems? If so name some models that you think would pass such a test and some that you think might not.<br />
<br />
Submitted by Laurie Snell<br />
<br />
==Societies worse off when they have God on their side==<br />
<br />
[http://www.timesonline.co.uk/article/0,,2-1798944,00.html Societies worse off when they have God on their side]<br><br />
Timesonline, September 27, 2005<br><br />
Ruth Gledhill<br />
<br />
[http://moses.creighton.edu/JRS/2005/2005-11.html Cross-national correlations of quantifiable societal health with popular religiosity and secularism in the prosperous democracies]<br><br />
Journal of Religion & Society, Vol.7(2005)<br><br />
Gregory S. Paul<br />
<br />
In the Times article we read:<br />
<br />
<blockquote>According to the study, belief in and worship of God are not only unnecessary for a healthy society but may actually contribute to social problems.<br><br><br />
Many liberal Christians and believers of other faiths hold that religious belief is socially beneficial, believing that it helps to lower rates of violent crime, murder, suicide, sexual promiscuity and abortion. The benefits of religious belief to a society have been described as its “spiritual capital”. But the study claims that the devotion of many in the US may actually contribute to its ills. <br />
</blockquote><br />
<br />
Gregory Paul is a dinosaur paleontologist and on an [http://www.abc.net.au/worldtoday/indexes/2005/twt_20050928.htm interview] on Australian ABC radio Paul said that, being a paleontologist, for many years he had to deal with the issue of creationism versus evolutionary science in the U.S and his interest in evolutionary science prompted him to look at whether there was any link between the religiosity of a society and how well that society functions. <br />
<br />
If you look at Paul's article you will find very little technical statistical analysis, for example, he did not carry out a regression analysis. Rather he rests his case on the series of scatterplots.<br />
<br />
Paul describes his data sources as:<br />
<br />
<blockquote>Data sources for rates of religious belief and practice as well as acceptance of evolution are the 1993 Environment I (Bishop) and 1998 Religion II polls conducted by the International Social Survey Program (ISSP), a cross-national collaboration on social science surveys using standard methodologies that currently involves 38 nations. The last survey interviewed approximately 23,000 people in almost all (17) of the developed democracies; Portugal is also plotted as an example of a second world European democracy. Results for western and eastern Germany are combined following the regions' populations. England is generally Great Britain excluding Northern Ireland; Holland is all of the Netherlands. The results largely agree with national surveys on the same subjects; for example, both ISSP and Gallup indicate that absolute plus less certain believers in a higher power are about 90% of the U.S. population. The plots include Bible literalism and frequency of prayer and service attendance, as well as absolute belief in a creator, in order to examine religiosity in terms of ardency, conservatism, and activities. </blockquote><br />
<br />
Here are the countries Paul considered with the abbreviations used on the graphics. <br />
<br />
A = Australia, C = Canada, D = Denmark, E = Great Britain, F = France, G = Germany,<br />
H = Holland, I = Ireland, J = Japan, L = Switzerland, N = Norway, P = Portugal, R = Austria,<br />
S = Spain, T = Italy, U = United States, W = Sweden, Z = New Zealand.<br />
<br />
There seems to be no agreement as to which countries are developed democracies. For example Paul might have included Greece and Belgium, Finland, and others but the data may have determined his choice. Paul comments that he added Portugal as an example of a second world democracy. <br />
<br />
Paul's anaysis of the data includes a series of 9 Figures which are available at the end of the article and are the most interesting part of the study. If you try printing Paul's article you will only get the first of his 9 Figures. When you look at the [http://moses.creighton.edu/JRS/2005/2005-11.html web version] you will still see only Figure 1 but the others can be viewed by selecting the numbers from 2 to 9 on the left side of Figure 1.<br />
<br />
Figure 1 deals with the proportion of people who accept human evolution which is interesting but not as relevant to the welfare of the people as others so we will look at Figure 2.<br />
<br />
[[Image:religion2.png|500px|center|Source:Gregory Paul]]<br />
<br />
Each Figure iprovides 5 separate scatterplots. Ïn Figure 2 we see that the U.S. has largest number--between 6 and 7-- of homicides per 100,000 and Spain has the lowest number with less than 1 homicide per 100,000. We also see that the U.S. has the highest proportion of people, about 25%, who take the bible literally while several countries have less than 10% such people.<br />
<br />
What we cannot do is compare the number of homicides per thousand between those who take the bible literally and those who are agnostics or atheists which is what we would really want to know. Presumably the data did not permit this comparison. <br />
<br />
[[Image:religion3.png|500px|center|Source:Gregory Paul]]<br />
<br />
Figure 3 deals with "14-24 year old suicides per 100,000". Here the U.S. is in about the middle.<br />
<br />
Figure 4 deals with the "under-five mortalities per 1000 births".<br />
<br />
[[Image:religion4.png|500px|center|Source:Gregory Paul]]<br />
<br />
Ignoring Portugal, the U.S. has the highest number of under-five mortalities per 1000 births-- between 7 and--8 while several countries have only 4.<br />
<br />
The other figures can be seen at end of Paul's article. They deal with life expectancy, sexually transmitted diseases, abortion and 15-16 year old pregnancies. Life expectancy is the smallest in the U.S. and for sexually transmitted diseases, abortion and 15-17 year old prenacies the U.S. is at the top of the graphs and in fact these look like outliers.<br />
<br />
Well, this study does not by itself justify the Times hedline: "Societies worse off when they have God on their side." Paul himself would not claim this. He writes:<br />
<br />
<blockquote> This study is a first, brief look at an important subject that has been almost entirely neglected by social scientists. The primary intent is to present basic correlations of the elemental data. Some conclusions that can be gleaned from the plots are outlined. This is not an attempt to present a definitive study that establishes cause versus effect between religiosity, secularism and societal health. It is hoped that these original correlations and results will spark future research and debate on the issue.</block<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div></div>Nano12https://www.causeweb.org/wiki/chance/index.php?title=Chance_News_7&diff=1535Chance News 72005-11-05T09:32:54Z<p>Nano12: /* Understanding probability */</p>
<hr />
<div>Sept 26 2005 to Oct 15 2005<br />
==Quotation==<br />
<blockquote><br />
While writing my book [Stochastic Processes] I had an argument with Feller [Introuction to Probability Theory and its Applications]. He asserted that everyone said "random variable" and I asserted that everyone said "chance variable." We obviously had to use the same name in our books, so we decided the issue by a stochastic procedure. That is, we tossed for it and he won. </blockquote><br />
<br />
<p align = right> Joe Doob<br><br />
[http://www.dartmouth.edu/~chance/Doob/conversation.html Statistical Science]<br><br />
<br />
==Forsooth==<br />
<br />
Peter Winkler suggested our first forsooth.<br />
<br />
<blockquote>Texas beats Ohio State in their opening game <br />
of the season (Saturday Sept 10 2002). The sportscasters (legendary Brent Musburger on play-by-play or Gary Danielson on analysis) observed that of the 14 teams who have <br />
previously played in the championship game (at the end of each season) 5 <br />
have suffered an earlier defeat. "Thus," they conclude, "Ohio State can <br />
still make it to the championship game, but their chances are now less <br />
than 50%."</blockquote><br />
<br />
===Discussion===<br />
<br />
What is wrong with this?<br />
----<br />
Here are forsooths from the September 2005 issues of RSS NEWS<br />
<br />
<blockquote>'Big ticket quiz' at the start of Wimbledon:<br><br><br />
Q. How many punnets (a small light basket or other container for fruit or vegetables) of strawberries are eaten each day during the Wimbledon tournament?<br><br />
Is it (a) over 8,000, (b) over 9,000 or (c) over 10,000?</blockquote><br />
<br />
<div align="right">BBC radio 5<br><br />
20 June 2005</div><br />
<br />
<blockquote>Waiting time for foot surgery down by 500%</blockquote><br />
<br />
<div align="right">Evening News (Edinburgh)<br><br />
5 July 2005</div><br />
<br />
The next two forsooths are from the October RSS news.<br />
<br />
<blockquote>In 1996-8 when the number attending university was static, the participation of women was also static, but male participation fell.</blockquote><br />
<br />
<div align="right">The Times Higher<br><br />
21 January 2005</div><br />
<br />
<blockquote>[On the subject of congestion on the London Underground..] 'Last year 976 million of us used the tube...'</blockquote><br />
<br />
<div align="right">BBC London News<br><br />
19 May 2005</div><br />
<br />
<br />
==Fortune's Formula==<br />
<br />
''Fortune's Formula: Wanna Bet?''<br><br />
''New York Times Book Section'', September 25, 2005<br><br />
David Pogue<br />
<br />
This must be the kind of review that every Science writer dreams of. Pogue ends his review with:<br />
<br />
<blockquote> ''Fortune's Formula'' may be the world's first history book, gambling primer, mathematics text, economics manual, personal finance guide and joke book in a single volume. Poundstone comes across like the best college professor you ever had, someone who can turn almost any technical topic into an entertaining and zesty lecture. But every now and then, you can't help wishing there were some teaching assistants on hand to help.</blockquote><br />
<br />
The author William Poundstone is a science writer who has written a number of very successful science books. His book, ''Prisoner's dilemma: John von Neumann, game theory and the puzzle of the bomb'', was written in the style of this book. Indeed Helen Joyce, in her review of this book in Plus Magazine writes:<br />
<br />
<blockquote>This book is a curious mixture of biography, history and mathematics, all neatly packaged into an entertaining and enlightening read. </blockquote><br />
<br />
Poundstone describes himself as a visual artist who does books as a "day job.". You can learn about his art work [http://www.uiowa.edu/~iareview/tirweb/feature/poundstone/interview2.htm here].<br />
<br />
''Fortune's Formula'' is primarily the story of Edward Thorp, Claude Shannon, and John Kelly and their attempt to use mathematics to make money gambling in casinos and on the stock market. None of these did their graduate work in mathematics. Thorp and Kelly got their Phd's in physics and Shannon in Genetics. <br />
<br />
In the spring of 1955, while a graduate student at UCLA, Thorp joined a discussion on the possiblity of making money from roulette. Thorp suggested that they could taking advantage of the fact that bets are still accepted for a few second after the croupier releases the ball, and in these seconds, he could estimate what part of the wheel the ball would stop. <br />
<br />
Thorp did not pursue this and in 1959 became an instructor in mathematics at M.I.T. Here he became interested in blackjack and developed his famous card counting method for wining at blackjack. He decided to publish his method in the most prestigious journal he could find and settled on ''Proceedings of the National Academy of Sciences''. For this he needed to have a member of the Academy submit his paper. The only member in the math department was Shannon so he had to persuade him of the importance of his paper. Shannon not only agreed but in the process became fascinated by Thorp's idea for beating roulette. He agreed to help Thorp carry this out. They built a roulette machine in Shannon's basement. It worked fine there in trial runs but not so well in the casino so they did not pursue this method of getting rich. <br />
<br />
Of course Thorp is best known for showing that blackjack is a favorable game and giving a method to exploit this fact. Shannon is best known for his work in information theory. Kelly is known his method for gambling in a favorable game. This plays a central role in Poundstone's book and is probably why Pogue felt that it would help if he had a teaching assistant. Poundstone tries to explain Kelly's work in many different ways but what he really needed to understand it is an example but this required too many formulas for a popular book. So we shall include an example from Chance News 7.09. <br />
<br />
Writing for Motley Fool, 3 April 1997 Mark Brady complained about the inumeracy of the general public and gave a number of examples including this one:<br />
<br />
<blockquote> Fear of uncertainty and innumeracy are synergistic. Most people cannot do the odds. What is a better deal over a year? A 100% safe return with 5 percent interest or a 90 percent safe return with a 20 percent return. For the first deal, your return will be 5% percent. For the second, your return will be 8%. Say you invest $1000 10 times. Your interest for the 9 successful deals will be 9000 x 0.2 or 1800. Subtract the 1000 you lost on the 10th deal and you get a $800 return on your original $10,000 for 8 percent.</blockquote><br />
<br />
Peter Doyle suggested that a better investment strategy in this case is:<br />
<br />
Faced with a 100 percent-safe investment returning 5 percent and a 90 percent-safe investment returning 20%, you should invest 20% of your funds in the risky investment and 80% in the safe investment. This gives you an effective return of roughly 5.31962607969968292 percent. <br />
<br />
Peter is using a money management system due to J. L. Kelly (1956: "A new interpretation of information rate," ''Bell System Technical Journal'', '''35'''). Kelly was interested in finding a rational way to invest your money faced with one or more investment schemes, each of which has a positive expected gain. He did not think it reasonable to try simply to maximize your expected return. If you did this in the Motley Fools example as suggested by Mark Brady, you would choose the risky investment and might well lose all your money the first year. We will illustrate what Kelly did propose in terms of Motley Fools example. <br />
<br />
We start with an initial capital, which we choose for convenience to be $1, and invest a fraction r of this money in the gamble and a fraction 1-r in the sure-thing. Then for the next year we use the same fractions to invest the money that resulted from the first year's investments and continue, using the same r each year. Assume, for example, that in the first and third years we win the gamble and in the second year we lose it. Then after 3 years our investment returns an amount f(r) where: <br />
<br />
<math><br />
f(r) = (1.2r + 1.05(1-r))(1.05(1-r))(1.2r + 1.05(1-r)). <br />
</math><br />
<br />
After n years, we would have n such factors, each corresponding to a win or a loss of our risky investment. Since the order of the terms does not matter our capital will be: <br />
<br />
<math><br />
f(r,n) = (1.2r + 1.05(1-r))^W(1.05(1-r))^L<br />
</math><br />
<br />
where W is the number of times we won the risky investment and L the number of times we lost it. Now Kelly calls the quantity:<br />
<br />
<math><br />
G(r) =\lim_{n \to \infty }\frac{\log(f( r,n)} {n}<br />
</math> <br />
<br />
the exponential rate of growth of our capital. In terms of G(r) our capital should grow like <math> e^{G(r)} </math>. In our example: <br />
<br />
<math><br />
\log(\frac{f(r,n)}{n}) = \frac{W}{n}\log(1.2r + 1.05(1-r)) + \frac{L}{n}\log(1.05(1-r))<br />
</math> <br />
<br />
Since we have a 90% chance of winning our gamble, the [http://en.wikipedia.org/wiki/Strong_law_of_large_numbers#The_strong_law strong law of large numbers] tells us that as n tends to infinity this will converge to <br />
<br />
<math><br />
G(r) = 0.9\log(1.2r + 1.05(1-r))+0.1\log(1.05(1-r))<br />
</math><br />
<br />
It is a simple calculus problem to show that G(r) is maximized by r = 0.2 with: <br />
G(0.2) = 0.05183. Then e^{0.05183} = 1.0532, showing that our maximum rate of growth is 5.32% as claimed by Peter. <br />
<br />
The attractiveness of the Kelly investment scheme is that, in the long run, any other investment strategy (including those where you are allowed to change your investment proportions at different times) will do less well. "In the long run and less well" means more precisely that the ratio of your return under the Kelly scheme and your return under any other strategy will tend to infinity.<br />
<br />
Thorp had a very good experience in the stock market, which is described very well by Gaeton Lion in his excellent [http://www.amazon.com/gp/product/customer-reviews/0809046377/ref=cm_cr_dp_pt/103-8647004-5865443?%5Fencoding=UTF8&n=283155&s=books review] of ''Fortune's Formula''. He writes:<br />
<br />
<blockquote> Ed Thorp succeeded in deriving superior returns in both gambling and investing. But, it was not so much because of Kelly's formula. He developed other tools to achieve superior returns. In gambling, Ed Thorp succeeded at Black Jack by developing the card counting method. He just used intuitively Kelly's formula to increase his bets whenever the odds were in his favor. Later, he ran a hedge fund for 20 years until the late 80s and earned a rate of return of 14% handily beating the market's 8% during the period. <br><br><br />
<br />
Also, his hedge fund hardly lost any value on black Monday in October 1987, when the market crashed by 22%. The volatility of his returns was far lower than the market. He did this by exploiting market inefficiencies using warrants, options, and convertible bonds. The Kelly formula was for him a risk management discipline and not a direct source of excess return. </blockquote><br />
<br />
Shannon also made a lot of money on the stock market, but did not use Kelly's formula. In his [http://www.amazon.com/gp/product/customer-reviews/0809046377/ref=cm_cr_dp_pt/103-8647004-5865443?%5Fencoding=UTF8&n=283155&s=books review] Gaeton Lion writes<br />
<br />
<blockquote>Claude Shannon amassed large wealth by recording one of the best investment records. His performance had little to do with Kelly's formula. Between 1966 and 1986, his record beat even Warren Buffet (28% to 27% respectively). Shannon strategy was similar to Buffet. Both their stock portfolios were concentrated, and held for the long term. Shannon achieved his record by holding mainly three stocks (Teledyne, Motorola, and HP). The difference between the two was that Shannon invested in technology because he understood it well, while Buffet did not. </blockquote><br />
<br />
Finally, Thorp provided the following comments for the book cover:<br />
<br />
<blockquote>From bookies to billionaires, you'll meet a motley cast of characters in this highly original, 'outside the box' look at gambling and investing. Read it for the stories alone, and you'll be surprised at how much else you can learn without even trying. --Edward O. Thorp, author of ''Beat the Dealer'' and ''Beat the Market''.</blockquote><br />
<br />
Submitted by Laurie Snell.<br />
<br />
<br />
==Which foods prevent cancer?==<br />
<br />
Which of these foods will stop cancer? (Not so fast)<br><br />
New York Times, 27 September 2005, Sect. F, p. 1<Br><br />
Gina Kolata<br />
<br />
Among other examples, the article includes a [http://www.nytimes.com/imagepages/2005/09/26/science/20050927_CANCER_GRAPHIC.html data graphic] on purported benefits of dietary fiber in preventing colorectal cancer. Early observational studies indicated an association, but subsequent randomized experiments found no effect. <br />
<br />
More to follow.<br />
<br />
<br />
==Slices of risk and the <em>broken heart</em> concept==<br />
[http://www.gloriamundi.org/picsresources/news20050912.pdf How a Formula Ignited Market That Burned Some Big Investors],<br />
Mark Whitehouse, The Wall Street Journal, September 12, 2005.<br><br />
<br />
This on-line article relates how a statistician, David Li,<br />
unknown outside a small coterie of finance theorists, helped change the world of investing. <br />
<br />
The article focuses on a event last May when General Motors Corp's debt<br />
was downgraded to junk status, causing turmoil in some financial markets.<br />
The article gives a nice summary of the underlying financial instruments known<br />
as credit derivatives -<br />
investment contracts structured so their value depends on the behavior of some other thing or event -<br />
with exotic names like <br />
[http://en.wikipedia.org/wiki/Collateralized_debt_obligations collateralized debt obligations] and [http://en.wikipedia.org/wiki/Credit_default_swap credit-default swaps].<br />
<br />
The critical step is to estimate the likelihood that many of the companies <br />
in a pool of companies would go bust at once. <br />
For instance, if the companies were all in closely related industries,<br />
such as auto-parts suppliers, they might fall like dominoes after a catastrophic event.<br />
Such a pool would have a 'high default correlation'.<br />
<br />
In 1997, nobody knew how to calculate default correlations with any precision. <br />
Mr. Li's solution drew inspiration from a concept in actuarial science known as the <br />
<em>broken heart</em> syndrome - people tend to die faster after the death of a beloved spouse. <br />
Some of his colleagues from academia were working on a way to predict this<br />
death correlation, something quite useful to companies that sell life insurance and joint annuities.<br />
He says:<br />
<blockquote><br />
Suddenly I thought that the problem I was trying to solve was exactly like the problem these<br />
guys were trying to solve,.<br />
Default is like the death of a company, so we should<br />
model this the same way we model human life."<br />
</blockquote><br />
<br />
This gave him the idea of using [http://en.wikipedia.org/wiki/Copula_%28statistics%29 copulas], <br />
mathematical functions the colleagues had begun applying to actuarial science. <br />
Copulas help predict the likelihood of various events<br />
occurring when those events depend to some extent on one another. <br />
Until the events last May of this year, one of the most popular copulas for bond pools <br />
was the Gaussian copula, named after <br />
[http://en.wikipedia.org/wiki/Carl_Friedrich_Gauss Carl Friedrich Gauss], a 19th-century German statistician. <br />
<br />
===Further reading===<br />
* The [http://www.gloriamundi.org/picsresources/news20050912.pdf on-line article] gives more details about what went wrong in the financial markets in May and the search for a more appropriate copula to capture better the <em>broken heart</em> syndrome between companies.<br />
* [http://en.wikipedia.org/wiki/Wikipedia Wikipedia] is a very worthwhile on-line resource for definitions of technical words, such as [http://en.wikipedia.org/wiki/Copula_%28statistics%29 copula].<br />
<br />
Submitted by John Gavin.<br />
<br />
<br />
==Learning to speak via statistics and graph theory==<br />
<br />
[http://education.guardian.co.uk/tefl/teaching/story/0,15085,1576100,00.html Computer learns grammar by crunching sentences], Max de Lotbinière September 23, 2005, [http://www.guardianweekly.co.uk/ Guardian Weekly].<br><br />
[http://www.cornellsun.com/vnews/display.v/ART/2005/09/09/432118a84f6af Profs’ New Software ‘Learns’ Languages], Ben Birnbaum, 9 Sep 2005, Cornell Daily Sun.<br />
<br />
A language-learning robot may sound like science fiction but new software, developed by Cornell University psychology professor Shimon Edelman, with colleagues Zach Solan, David Horn and Eytan Ruppin from Tel Aviv University in Israel, is well on the way to constructing a computer program that can teach itself languages and make up its own sentences, the developers' claim.<br />
<br />
Unlike previous attempts at developing computer algorithms for language learning - "Automatic Distillation of Structure," or "ADIOS" for short - discovers complex patterns in raw text by repeatedly aligning sentences and looking for overlapping parts.<br />
Once it has derived a language's rules of grammar,<br />
it can then produce sentences of its own, simply from blocks of text in that language.<br />
<br />
It has been evaluated on artificial context-free grammars with thousands of rules, <br />
on natural languages as diverse as English and Chinese, <br />
on coding regions in DNA sequences and on protein data correlating sequence with function. <br />
<br />
Edelman comments:<br />
<blockquote><br />
Adios relies on a statistical method for pattern extraction and on structured generalisations <br />
- the two processes that have been implicated in language acquisition.<br />
Our experiments show that Adios can acquire intricate structures <br />
from raw data including transcripts of parents' speech directed at two- or three-year-olds.<br />
This may eventually help researchers understand how children, <br />
who learn language in a similar item-by-item fashion, and with little supervision, <br />
eventually master the full complexity of their native tongue.<br />
</blockquote><br />
<br />
[http://plus.maths.org/latestnews/may-aug05/adios/ Plus Magazine's website]<br />
offers a more logical explanation:<br />
<blockquote><br />
The ADIOS algorithm is based on statistical and algebraic methods performed on one of the most basic and versatile objects of mathematics - the graph.<br />
Given a text, the program loads it as a graph by representing each word by a node, or vertex, and each sentence by a sequence of nodes connected by lines. A string of words in the text is now represented by a path in the graph. <br><br />
<br />
Next it performs a statistical analysis to see which paths, or strings of words, occur unusually often. <br />
It then decides that those that appear most frequently - called "significant patterns" - <br />
can safely be regarded as a single unit<br />
and replaces the set of vertices in each of these patterns by a single vertex, <br />
thus creating a new, generalised, graph.<br><br />
<br />
Finally, the program looks for paths in the graph which just differ by one vertex. <br />
These stand for parts of sentences that just differ by one word (or compound of words) like "the cat is hungry" and "the dog is hungry". <br />
Performing another statistical test on the frequency of these paths, the program identifies classes of vertices, or words, that can be regarded as interchangeable, or equivalent. <br />
The sentence involved is legitimate no matter which of the words in the class - in our example "cat" or "dog" - you put in.<br><br />
<br />
This last step is then repeated recursively.<br><br />
</blockquote><br />
<br />
[http://plus.maths.org/latestnews/may-aug05/adios/ The website] uses graphs to illustrate some examples and it finishes with some reassuring words:<br />
<blockquote><br />
All this doesn't mean, of course, that the program actually "understands" what it's saying. It simply knows how to have a good go at piecing together fragments of sentences it has identified, in the hope that they are grammatically correct. So if, like me, you're prone to swearing at your computer, you can safely continue to do so: it won't answer back for a long while yet.<br />
</blockquote><br />
<br />
===Further reading===<br />
The [http://adios.tau.ac.il/ ADIOS homepage] offers an overview and more detailed description of the program.<br />
<br />
Submitted by John Gavin.<br />
<br />
==Understanding probability==<br />
<br />
Understanding Probability:Chance rules in everyday life<br><br />
Cambridge University Press 2004<br><br />
Henk Tijms<br />
<br />
Hank Tijms is Professor in Operation Research at the Vrije University in Amsterdam. This book is based on his earlier Dutch book “Spelen met Kansen.” <br />
<br />
The aim of this book is to show how probability applies to our everyday life in a way that your Uncle George could understand even if he has forgotten much of his high school math. Tijms does not try to avoid mathematics but only to postpone the formal math until the reader has seen the many applications of probability in the real world, how much fun it is, and learned to work problems and when he can’t work one how to get the answer by simulation. He learns all this in part I of the book and then he learns the more formal math in Part II.<br />
<br />
In Chapter 1 Tijms asks the reader to think about problems with surprising answers in the spirit of Susan Holmes “[http://www-stat.stanford.edu/~susan/surprise/ Probability by Surprise]” including the birthday problem and the Monty Hall problem. Readers are on their own to try to solve one or more of the problems but promised that they will see the solutions later in the book. <br />
<br />
Chapter 2 deals with the law of large numbers and introduces the concept of simulation. This theorem is explained and illustrated by problems related, for example, to coin tossing, random walks and casino games. Expected value is introduced in an informal way to be defined more carefully later in the book. For the reader who is not frightened by mathematical formulas, Tijms includes a discussion of the Kelly betting system with a footnote saying that this paragraph can be skipped at first reading. This is a fascinating topic that is widely applied in gambling and stock investment but rarely appears in a probability book.<br />
<br />
In Chapter 3 the author returns to previous problems such as the birthday problem and gambling systems and solves them first by simulation and then by mathematics. <br />
<br />
In this chapter Tijms describes Efron’s bootstrap method and uses it to solve a number of problems including a hypothetical clinical trial and to test if the famous 1970 draft lottery during the Vietnam War was fair. Again the bootstrap method has wide application but rarely occurs in an elementary probability or statistics book.<br />
<br />
Chapter 4 describes the binomial, Poisson, and hypergeomtric distributions and how to use them in solving problems such as the famous hat check problem, and a variety of interesting lottery questions. The Poisson process is discussed but again with the footnote that novice readers might want to read this at a later time.<br />
<br />
Chapter 5 is mainly about Center Limit Theorem and its many applications especially to statistics. <br />
<br />
Chapter 6 introduces Chance trees and Bayes’s rule. The tree method is used to explain a variety of problems including the Monty Hall Problem and the false-positive paradox. <br />
<br />
This is a brief description of the first six chapters which constitute Part I of the book. Now the fun is over. Part 2 called “Essentials of probability” looks like the traditional first chapters in a standard probability book. But the reader has already found how exciting probability is, has a good intuitive idea of the basic concepts and has worked many of the interesting problems at the end of each chapter either using math or simulation. For some students this might allow them to actually enjoy Part 2. But your Uncle George may want to quit while they are ahead. <br />
<br />
Tijms writes with great clarity and his enthusiasm for probability in the real world is contagious. We were delighted to see, as acknowledged in the preface, that Tijms included several of the more interesting problems discussed in Chance News, often going well beyond what we had said in our discussion of the problem. <br />
<br />
This book presents a completely new way to go about teaching a first course in probability and we think those who teach such a course should consider trying it out.<br />
<br />
===Discussion===<br />
<br />
(1) In the days of Basic we required all students to learn Basic in their first math course so we could assume that students could write programs to simulate probability problems and so me made heavy use of simulation as suggested in this book. The author uses Pascal in his book. What present language do you think is easiest for a student with no computing experience to learn?<br />
<br />
We asked Professor Tijms what the situation was in math departments in Europe and he replied:<br />
<br />
<blockquote>In math departments of universities and polytechnic schools in Europe students learn to write computer programs. In my university they still learn to program in Java and C++ ( in previous days Pascal), but I see in the Netherlands the trend that the instructors think it is sufficient if the students are able to program in Matlab. <br><br><br />
<br />
In ny book I have chosen to formulate the simulation programs in Pascal because of the clarity and the simplicity of the language, though this language is hardly used anymore. The introductory probability course at my university is given before they have learned to program, but this does not prevent them of simulating probability problems by using Excel. In the simulation of many elementary probability problems a random-number generator alone suffices to simulate those problems and so Excel can be used. In the second year they have mastered Matlab, a perfect tool with its excellent graphics to simulate many challenging probability problems ( they really like it, in particular when it concerns problems such as the problems 2.24-2.45 in chapter 2 and the problems 5.11-5.13 in chapter 5). <br />
</blockquote><br />
<br />
<br />
(2) Do you think that probability books should include data to test probability models that are said to describe real world problems? If so name some models that you think would pass such a test and some that you think might not.<br />
<br />
Submitted by Laurie Snell<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div><br />
<br />
==Societies worse off when they have God on their side==<br />
<br />
[http://www.timesonline.co.uk/article/0,,2-1798944,00.html Societies worse off when they have God on their side]<br><br />
Timesonline, September 27, 2005<br><br />
Ruth Gledhill<br />
<br />
[http://moses.creighton.edu/JRS/2005/2005-11.html Cross-national correlations of quantifiable societal health with popular religiosity and secularism in the prosperous democracies]<br><br />
Journal of Religion & Society, Vol.7(2005)<br><br />
Gregory S. Paul<br />
<br />
In the Times article we read:<br />
<br />
<blockquote>According to the study, belief in and worship of God are not only unnecessary for a healthy society but may actually contribute to social problems.<br><br><br />
Many liberal Christians and believers of other faiths hold that religious belief is socially beneficial, believing that it helps to lower rates of violent crime, murder, suicide, sexual promiscuity and abortion. The benefits of religious belief to a society have been described as its “spiritual capital”. But the study claims that the devotion of many in the US may actually contribute to its ills. <br />
</blockquote><br />
<br />
Gregory Paul is a dinosaur paleontologist and on an [http://www.abc.net.au/worldtoday/indexes/2005/twt_20050928.htm interview] on Australian ABC radio Paul said that, being a paleontologist, for many years he had to deal with the issue of creationism versus evolutionary science in the U.S and his interest in evolutionary science prompted him to look at whether there was any link between the religiosity of a society and how well that society functions. <br />
<br />
If you look at Paul's article you will find very little technical statistical analysis, for example, he did not carry out a regression analysis. Rather he rests his case on the series of scatterplots.<br />
<br />
Paul describes his data sources as:<br />
<br />
<blockquote>Data sources for rates of religious belief and practice as well as acceptance of evolution are the 1993 Environment I (Bishop) and 1998 Religion II polls conducted by the International Social Survey Program (ISSP), a cross-national collaboration on social science surveys using standard methodologies that currently involves 38 nations. The last survey interviewed approximately 23,000 people in almost all (17) of the developed democracies; Portugal is also plotted as an example of a second world European democracy. Results for western and eastern Germany are combined following the regions' populations. England is generally Great Britain excluding Northern Ireland; Holland is all of the Netherlands. The results largely agree with national surveys on the same subjects; for example, both ISSP and Gallup indicate that absolute plus less certain believers in a higher power are about 90% of the U.S. population. The plots include Bible literalism and frequency of prayer and service attendance, as well as absolute belief in a creator, in order to examine religiosity in terms of ardency, conservatism, and activities. </blockquote><br />
<br />
Here are the countries Paul considered with the abbreviations used on the graphics. <br />
<br />
A = Australia, C = Canada, D = Denmark, E = Great Britain, F = France, G = Germany,<br />
H = Holland, I = Ireland, J = Japan, L = Switzerland, N = Norway, P = Portugal, R = Austria,<br />
S = Spain, T = Italy, U = United States, W = Sweden, Z = New Zealand.<br />
<br />
There seems to be no agreement as to which countries are developed democracies. For example Paul might have included Greece and Belgium, Finland, and others but the data may have determined his choice. Paul comments that he added Portugal as an example of a second world democracy. <br />
<br />
Paul's anaysis of the data includes a series of 9 Figures which are available at the end of the article and are the most interesting part of the study. If you try printing Paul's article you will only get the first of his 9 Figures. When you look at the [http://moses.creighton.edu/JRS/2005/2005-11.html web version] you will still see only Figure 1 but the others can be viewed by selecting the numbers from 2 to 9 on the left side of Figure 1.<br />
<br />
Figure 1 deals with the proportion of people who accept human evolution which is interesting but not as relevant to the welfare of the people as others so we will look at Figure 2.<br />
<br />
[[Image:religion2.png|500px|center|Source:Gregory Paul]]<br />
<br />
Each Figure iprovides 5 separate scatterplots. Ïn Figure 2 we see that the U.S. has largest number--between 6 and 7-- of homicides per 100,000 and Spain has the lowest number with less than 1 homicide per 100,000. We also see that the U.S. has the highest proportion of people, about 25%, who take the bible literally while several countries have less than 10% such people.<br />
<br />
What we cannot do is compare the number of homicides per thousand between those who take the bible literally and those who are agnostics or atheists which is what we would really want to know. Presumably the data did not permit this comparison. <br />
<br />
[[Image:religion3.png|500px|center|Source:Gregory Paul]]<br />
<br />
Figure 3 deals with "14-24 year old suicides per 100,000". Here the U.S. is in about the middle.<br />
<br />
Figure 4 deals with the "under-five mortalities per 1000 births".<br />
<br />
[[Image:religion4.png|500px|center|Source:Gregory Paul]]<br />
<br />
Ignoring Portugal, the U.S. has the highest number of under-five mortalities per 1000 births-- between 7 and--8 while several countries have only 4.<br />
<br />
The other figures can be seen at end of Paul's article. They deal with life expectancy, sexually transmitted diseases, abortion and 15-16 year old pregnancies. Life expectancy is the smallest in the U.S. and for sexually transmitted diseases, abortion and 15-17 year old prenacies the U.S. is at the top of the graphs and in fact these look like outliers.<br />
<br />
Well, this study does not by itself justify the Times hedline: "Societies worse off when they have God on their side." Paul himself would not claim this. He writes:<br />
<br />
<blockquote> This study is a first, brief look at an important subject that has been almost entirely neglected by social scientists. The primary intent is to present basic correlations of the elemental data. Some conclusions that can be gleaned from the plots are outlined. This is not an attempt to present a definitive study that establishes cause versus effect between religiosity, secularism and societal health. It is hoped that these original correlations and results will spark future research and debate on the issue.</block<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div></div>Nano12https://www.causeweb.org/wiki/chance/index.php?title=ChanceWiki:About&diff=1575ChanceWiki:About2005-11-05T09:32:39Z<p>Nano12: </p>
<hr />
<div>The Chance Wiki provides reviews of articles in the media that use probability or statistical concepts (chance news). It's purpose is to help the general public better understand chance news and also to allow teachers of probability or statistics to use current chance news in their courses.<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div></div>Nano12https://www.causeweb.org/wiki/chance/index.php?title=ChanceWiki:Community_Portal&diff=1571ChanceWiki:Community Portal2005-11-05T09:32:32Z<p>Nano12: </p>
<hr />
<div><br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div></div>Nano12https://www.causeweb.org/wiki/chance/index.php?title=File:News.gif&diff=1578File:News.gif2005-11-05T09:31:57Z<p>Nano12: </p>
<hr />
<div>This image is from the original chance news and was made by Fuxing Hou.<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div></div>Nano12https://www.causeweb.org/wiki/chance/index.php?title=Previous_Chance_News&diff=1568Previous Chance News2005-11-05T09:31:48Z<p>Nano12: </p>
<hr />
<div>*[[Chance News 1]]: May 1 2005 to May 31 2005<br />
*[[Chance News 2]]: June 1 2005 to June 30 2005<br />
*[[Chance News 3]]: July 1 2005 to July 31 2005<br />
*[[Chance News 4]]: Åug 1 2005 to Aug 30 2005<br />
*[[Chance News 5]]: Sep 1 2005 to Sept 14 2005<br />
*[[Chance News 6]]: Sept 15 2005 to Sept 30 2005<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div></div>Nano12https://www.causeweb.org/wiki/chance/index.php?title=Chance_News_8&diff=1541Chance News 82005-11-05T09:31:18Z<p>Nano12: </p>
<hr />
<div>Oct 15 to Oct 30<br />
<br />
==Quotation==<br />
<blockquote>One more fagot of these adamantine bandages, is, the new science of Statistics. It is a rule, that the most casual and extraordinary events -- if the basis of population is broad enough -- become matter of fixed calculation. It would not be safe to say when a captain like Bonaparte, a singer like Jenny Lind, or a navigator like Bowditch, would be born in Boston: but, on a population of twenty or two hundred millions, something like accuracy may be had. Ralph Waldo Emerson Fate</blockquote><br />
<br />
==Forsooth==<br />
Here's another Forsooth from the October issue of RSS News.<br />
<blockquote>Your'e more likely to die in a fire in Strathclyde than anywhere else in the country</blockquote><br />
<br />
<div align="right">BBC1 mews bullietin<br><br />
11 May 2005</div><br />
<br />
==The Poisson distribution and the Supreme Court==<br />
The Poisson distribution and the Supreme Court<br><br />
''Journal of the American Statistical Association'' 31, no. 195 ,(1936), 376-80<br><br />
W. Allen Wallis<br />
<br />
Supreme Court Appointments as a Poisson distribution<br><br />
''American Journal of Political Science'', 26, No.1, February 1982<br><br />
S. Sidney Ulmer<br />
<br />
This is not current news, but since Supreme Court appointments are in the news we felt that these articles might make an interesting class discussion.<br />
<br />
In 1936 statistician Allen Wallis suggested that a Poisson distribution can approximate the number of U.S. Supreme Court appointments in a given year. In his Table 1 Wallis provided the number appointed in each year over the intervals with different numbers of Justices on the Supreme Court: 1790-1806 (6) 1807-1836 (7), and 1837-1932 (9). Actually there were 10 in the years 1963 to 1967 which Wallis called "negligible exceptions."<br />
<br />
[[Image:wallis1.png|500px|center]]<br />
<br />
Wallis then restricts himself to the years 1837-1932 and finds that a Poisson distribution with mean .5 can approximate the number of court appointments in a year. His results are shown in his Figure II:<br />
<br />
[[Image:wallis2.png|500px|center]]<br />
<br />
In his article, Sidney Ulmer updated the data to 1980 and also includes data from the early Supreme Courts with 6 and 7 members. Thus his data covers the years 1790--1980. His Table 1 compares the actual number of appointments in a year with the expected number of appointments assuming a Poisson distribution with mean 5.13.<br />
<br />
[[Image:ulmer1.png|500px|center]]<br />
<br />
In his Table II Ulmer limits the data to the 9 member Supreme Courts: 1837 to 1862 and 1869-1980).<br />
<br />
[[Image:ulmer2.png|500px|center]]<br />
<br />
Testing the goodness of fits, Ulmer argues that the fit with the varying size Supreme Courts is just as good as with fixed size Supreme Courts.<br />
<br />
===DISCUSSION===<br />
<br />
(1) What is the probability that a President will make 2 or more appointments to the Supreme Court during a 4-year term? What is the probability a President makes no appointments during a 4-year term? Has this ever happened?<br />
<br />
(2) Do you agree with Ulmer that there is no reason to limit the data to years with the Supreme Court is the same size?<br />
<br />
(3) Obtain the data needed to update Ulmer's results to today and provide Tables that correspond to Ulmer's Tables 1 and 2. Add your Tables to this Chance News and make your data available to make it easier to update this in future years.<br />
<br />
Contributed by Laurie Snell<br />
<br />
==Possible Cancer Cluster in Connecticut==<br />
Pratt Agrees to Increase Funding for Brain Cancer Study <br><br />
''The Associated Press''<br><br />
October 11, 2005<br><br />
Stephen Singer<br><br />
<br />
<br />
In a case that seems eerily familiar to the leukemia cancer cluster made famous by the book and movie, ''A Civil Action'', researchers are trying to determine whether or not a cancer cluster exists among workers at Pratt & Whitney, a company that manufactures jet engines. Over one hundred former or current Pratt & Whitney employees have been identified as having a relatively rare type of fatal brain tumor known as glioblastoma multiforme, which strikes 3 people per 100,000 every year. Many of these workers have been exposed to metals and chemical substances, including TCE (trichloroethylene), which is an engine degreaser. TCE is the same carcinogenic chemical that was dumped in the 1960’s and 1970’s by the chemical company, WR Grace, in Woburn, MA, and that was found to have contaminated the drinking water in two of the town’s wells. <br><br />
<br />
<br />
Prior to the recent announcement that the funding is being increased from $6 million dollars to $12 million dollars, this medical study was already being described as the largest occupational health study ever conducted. It covers 250,000 people who worked at any of the seven Connecticut Pratt & Whitney plants from 1952 to 2001. So far, at least 125 cases of brain cancer have been documented, according to the lawyer who represents dozens of individuals and family members.<br><br />
<br />
<br />
The study falls under the auspices of the Connecticut Department of Public Health. However, due to the overwhelming cost and scope of the study, Pratt & Whitney is funding the project. Since Pratt is paying for the study, they chose the researchers, a team from the University of Pittsburgh. The project began three years ago, and the results are expected to be available between 2007 and 2009.<br><br />
<br />
<br />
In the meantime, this case faces many of the obstacles common in the quest to establish whether or not a cancer cluster exists, such as proving causation, the fact that it can take a long time (sometimes 5-40 years) after exposure for true problems to show up, and finding the people who were exposed & convincing them to participate in the study. Additionally, there are legal difficulties for the families involved, including Connecticut’s statute of limitations laws, the length of time it takes investigators to reach a conclusion, the cost of litigation, and the “deep pockets” of a company like Pratt & Whitney.<br><br />
<br />
<br />
This case study provides a current example of an ongoing investigation into a possible cancer cluster. Will it ultimately be found to be a coincidence cluster or proven to be a true cancer cluster? Does it make sense that the researchers are including in the study everyone who worked at Pratt over a fifty year period, even those who only worked there for a brief time period and those who were not directly exposed to toxic substances (i.e. office workers)? Could the researchers possibly have an unconscious bias in favor of the company that is funding their research? If the company doesn’t fund the research, then who should? Is there some other way to structure such investigations, so that the company involved pays for the study, but is not allowed to choose the researchers and directly fund them?<br><br />
<br />
<br />
'''Further Reading'''<br><br />
<br />
• “Rare Cancer Found in Workers”, ''The New York Times'', March 10, 2002, Jane Gordon<br><br />
• “Scientist: Pratt Commits to Cancer Study”, ''The Hartford Courant'', May 19, 2005<br><br />
• “Participation in Cancer Study at Pratt Lagging”, ''The Hartford Courant'', October 12, 2005, Paul Marks<br><br />
• ''The New Haven Advocate'' has had more than a dozen articles that explain the working conditions at Pratt & Whitney, and also chronicle the history & progression of this case. These articles have been investigated and written primarily by Carole Bass, Associate Editor. A few of the articles are listed below. <br> <br />
-“Worked to Death”, August 2, 2001, Carole Bass & Camille Jackson<br><br />
-“Talking Cure”, October 28, 2004, Dave Goldberg<br><br />
-“Time’s Not on Their Side”, January 20, 2005, Carole Bass<br><br />
-“The Brains Behind the Brain”, October 20, 2005, Carole Bass <br><br />
For the early New Haven Advocate articles (i.e., 2001-2002) on this subject, go to http://old.newhavenadvocate.com/workedtodeath/index.html<br> <br />
For the articles since 2002, go to <br><br />
http://www.newhavenadvocate.com and search for Pratt & Whitney.<br><br />
<br />
Submitted by Josephine Rodriguez.<br />
<br />
==A record powerball lottery jackpot==<br />
<br />
On Saturday Oct 22, 2005 the powerball lottery had a record powerball jackpot of 340 million dollars. <br />
<br />
When you buy a ticket for this lottery, you specify five distinct numbers from 1 to 55, which we call basic numbers and one number from 1 to 42 called the bonus number. To win the Jackpot your 5 basic numbers and your bonus number must agree with a random choice of 5 basic numbers and one bonus number chosen by the lottery officials. The number of possible tickets is:<br />
<br />
<center><math>{55 \choose 5} 42 = </math> 146,107,962</center><br />
<br />
Thus if you buy a single ticket, the probability of having a winning jackpot ticket is<br />
<br />
<center> <math>{1} \over {146107962}</math> = .000000006844...</center><br />
<br />
The powerball website and the media expresses this by saying that the odds that you have a winning jackpot ticket is 1 in 146,107,962. <br />
<br />
Whenever there is a record jackpot, the news writers look for suggestions for other rare events that might be more familiar to its readers. <br />
<br />
Our own favorite was suggested by Fred Hoppe: if you toss a coin 27 times your chance of getting 27 heads in a row is greater than your chance of having a winning jackpot ticket when you buy a single ticket. (<math> 2^{27} = 134217728</math> and so there are 134,217,728 possible sequences of heads and tails and only 1 has all heads.)<br />
<br />
In an article for the ''Omaha World-Herald'' Oct 18, 2005 , Robynn Tysver writes:<br />
<br />
<blockquote> You have a greater chance of getting killed by lightning than winning this week's 340 million Powerball jackpot. You also have a greater chance of drowning in a bathtub. The lifetime odds of getting killed by lightning are one in 56,439, and the lifetime odds of dying while in or falling into a bathtub are one in 10,582, according to the National Safety Council. <br />
</blockquote><br />
<br />
These are not even in the ballpark. The ''Minneapolis Star Tribune'' consulted mathematicians David Bressoud and Douglas Arnold who contributed the following:<br />
<br />
According to Arnold you have a seven times better chance of becoming a saint. And Bressoud notes that you're six times more likely to get elected president of the United States. But they also provide the following more interesting estimates:<br />
<br />
<blockquote>Bressoud: "If you buy 10 tickets a week, every week, it would take you 280,000 years before you could expect to win."<br><br><br />
<br />
Arnold: "If you were to select a group of Powerball numbers every minute for 138 years, you would have about a 50 percent chance of picking the winning Powerball ticket." <br><br><br />
<br />
It is not clear what Bressoud means by "expect to win". We can check this by a simple calculation (simple for Mathematica). Let q(n) be the probability that you if you buy n tickets you fail to get a winning jackpot ticket . Then:<br />
<br />
<center> <math> \left(\frac{146107961}{146107962}\right) ^n = q(n) </math></center><br />
<br />
The average number of weeks in a year is 52.177457 so If you buy 10 tickets a week, every week for 280,000 years you will buy about 146,097,000 tickets. Using this number for n in our formula we find that you have about a 37% chance of not getting a winning lottery ticket or a 63% chance of getting one. We would not "expect to win" with a 63% chance of winning but others may. Using our formula for q(n) we find that if we buy 10 tickets a week, every week for 830,000 years you will have about a 95% chance of getting at least one winning lottery ticket which seems to us more appropriate for expecting to win. <br />
<br />
Consider now Arnold's example. Our colleague Dana Williams found that you need to buy a ticket for about 101 million lottery offerings to have about a 50% chance of getting at least one winning lottery ticket. There are an average of 525,946.766 minutes in a year. Dividing 101 million by this number gives 192.035. Thus Arnold's 138 years should be 192 years.<br />
<br />
We asked Professor Arnold about this and he replied:<br />
<br />
<blockquote> That number, which was quoted in the ''Star Tribune'' was an off-the-top-of-my-head calculation made when the reporter called me on<br />
the phone with no warning. Right ballpark, but not very accurate. Later I redid the calculation carefully.</blockquote><br />
<br />
Arnold's computations were similar to ours but he used a greater accuracy for the number of independent lotteries you have to buy to have a 50% chance of choosing the jackpot numbers at least once. His answer to this was 101,274,322. Using this, Arnold's estimate for the number of years, buying a ticket every minute, to have a 50% chance of winning a jackpot is193 years instead of our estimate of 192 years.<br />
<br />
Arnold said that he also estimated the expected value of a $1 ticket. To do this he needed an estimate for the number of tickets sold. He was told that a reasonable estimate was 106 million. In calculating the expected value of a $1 ticket he used the cash value of 164.4 million dollars instead of the annuity payout of 340 million dollars. He also took into account the possibility of having to share the jackpot. Doing this he got an expected value of exactly $1, just the price of the ticket. He commented that if he took into account the taxes the expected value would be more like 80 cents making even this lottery an unfavorable event.<br />
<br />
The news writers also gave a lot of coverage of Senator Gregg (Chairman of the Senate Budget Committee) winning $853,492 for getting the second highest prize: getting the 5 basic numbers correct but note the bonus number. Normally the prize for getting this is $200,000 cash but Gregg was the beneficiary of recent change in the powerball lottery. <br />
<br />
The powerball officials have found that increasing the size of the jackpot can increase the ticket sales because of the public's interest in large jackpots. They do this by increasing the number of possible basic numbers. When they started in 1992, to get the jackpot you had to get the 5 basic numbers chosen from 45 numbers and the 1 bonus number chosen from 45 number correct. Here are the changes so far<br />
<br />
<center><br />
1992 5 of 45 1 of 45<br><br />
1997 5 or 49 1 of 42<br><br />
2002 5 of 55 1 of 42<br><br />
2005 5 of 55 1 of 42<br><br />
</center><br />
<br />
While the lottery officials want to have higher jackpots, they also do not want too long a period between jackpots. Normally the increase in the size of the lottery, when no one wins the jackpot, is determined by the amount taken in in this unsuccessful drawing. This was recently changed so that, when a new record jackpot occurs and no-one wins it, at most 25 million dollars are added to the Jackot until someone wins the jackpot. The money save by this is added to the second prize.<br />
<br />
When the 340 million jackpot was won, 49 players had the five basic numbers correct but not the bonus numbers. For these winners the $200,000 prize had 653,492 added to their prize so they each won $853,492. If they chosen the Powerball play option for an extra $1 their $200,000 would have been multiplied by 2,3,4, or 5 with equal probabilities. Thus if Gregg had chosen the Powerball play option, and been lucky, he would have won 1,653,492 dollars that he could add to his 15 or so million dollars he has in stocks. <br />
<br />
===DISCUSSION===<br />
<br />
(1) Do you think it is fair to advertise the lottery prize as 340 million when the cash prize is only 164.4 million?<br />
<br />
(2) What is the probability of winning the second prize?<br />
<br />
(3) Assuming that the estimate 106 million for the number of tickets sold find the expected number of second prize winners.<br />
<br />
==Mammograms Validated as Key in Cancer Fight==<br />
<br />
The ''New York Times'' [http://www.nytimes.com/2005/10/27/health/27breast.html reported] on October 27, 2005 on a new National Cancer Institute study that attributed a significant decrease in the death rate from breast cancer to mammogram screening tests. The study, published in the New England Journal of Medicine, found that from 28% to 65% of the sharp 24% decrease in breast cancer death rates from 1990 to 2000 was due to screening; the remainder was attributed to new drugs used to treat the disease.<br />
<br />
Prior to this study, the value of mammogram screening had been disputed, for several reasons. In the general population, the test results in a large proportion number of false positives, about 90%. Thus, many women who are cancer-free are subjected to unnecessary procedures. Also, approximately 30% of cancers that are detected and treated would not have progressed significantly. Unfortunately, it isn't possible to distinguish between these so-called ''indolent'' cancers and those that become life-threatening, so it is routine practice to treat them all.<br />
<br />
The new study suggests that the benefits of routine mammography are more certain than earlier believed, according to Don Berry, Chairman of the biostatistics department of M. D. Anderson Cancer Center, in Houston, Texas, and the lead author of the paper. He said that the new study for the first time properly separates the effects of therapy and screening. Nonetheless, he cautioned that mammography does pose risks, and recommended that women be counselled before screening.<br />
<br />
Contributed by Bill Jefferys<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div></div>Nano12https://www.causeweb.org/wiki/chance/index.php?title=Chance_News_7&diff=1534Chance News 72005-11-05T09:31:10Z<p>Nano12: </p>
<hr />
<div>Sept 26 2005 to Oct 15 2005<br />
==Quotation==<br />
<blockquote><br />
While writing my book [Stochastic Processes] I had an argument with Feller [Introuction to Probability Theory and its Applications]. He asserted that everyone said "random variable" and I asserted that everyone said "chance variable." We obviously had to use the same name in our books, so we decided the issue by a stochastic procedure. That is, we tossed for it and he won. </blockquote><br />
<br />
<p align = right> Joe Doob<br><br />
[http://www.dartmouth.edu/~chance/Doob/conversation.html Statistical Science]<br><br />
<br />
==Forsooth==<br />
<br />
Peter Winkler suggested our first forsooth.<br />
<br />
<blockquote>Texas beats Ohio State in their opening game <br />
of the season (Saturday Sept 10 2002). The sportscasters (legendary Brent Musburger on play-by-play or Gary Danielson on analysis) observed that of the 14 teams who have <br />
previously played in the championship game (at the end of each season) 5 <br />
have suffered an earlier defeat. "Thus," they conclude, "Ohio State can <br />
still make it to the championship game, but their chances are now less <br />
than 50%."</blockquote><br />
<br />
===Discussion===<br />
<br />
What is wrong with this?<br />
----<br />
Here are forsooths from the September 2005 issues of RSS NEWS<br />
<br />
<blockquote>'Big ticket quiz' at the start of Wimbledon:<br><br><br />
Q. How many punnets (a small light basket or other container for fruit or vegetables) of strawberries are eaten each day during the Wimbledon tournament?<br><br />
Is it (a) over 8,000, (b) over 9,000 or (c) over 10,000?</blockquote><br />
<br />
<div align="right">BBC radio 5<br><br />
20 June 2005</div><br />
<br />
<blockquote>Waiting time for foot surgery down by 500%</blockquote><br />
<br />
<div align="right">Evening News (Edinburgh)<br><br />
5 July 2005</div><br />
<br />
The next two forsooths are from the October RSS news.<br />
<br />
<blockquote>In 1996-8 when the number attending university was static, the participation of women was also static, but male participation fell.</blockquote><br />
<br />
<div align="right">The Times Higher<br><br />
21 January 2005</div><br />
<br />
<blockquote>[On the subject of congestion on the London Underground..] 'Last year 976 million of us used the tube...'</blockquote><br />
<br />
<div align="right">BBC London News<br><br />
19 May 2005</div><br />
<br />
<br />
==Fortune's Formula==<br />
<br />
''Fortune's Formula: Wanna Bet?''<br><br />
''New York Times Book Section'', September 25, 2005<br><br />
David Pogue<br />
<br />
This must be the kind of review that every Science writer dreams of. Pogue ends his review with:<br />
<br />
<blockquote> ''Fortune's Formula'' may be the world's first history book, gambling primer, mathematics text, economics manual, personal finance guide and joke book in a single volume. Poundstone comes across like the best college professor you ever had, someone who can turn almost any technical topic into an entertaining and zesty lecture. But every now and then, you can't help wishing there were some teaching assistants on hand to help.</blockquote><br />
<br />
The author William Poundstone is a science writer who has written a number of very successful science books. His book, ''Prisoner's dilemma: John von Neumann, game theory and the puzzle of the bomb'', was written in the style of this book. Indeed Helen Joyce, in her review of this book in Plus Magazine writes:<br />
<br />
<blockquote>This book is a curious mixture of biography, history and mathematics, all neatly packaged into an entertaining and enlightening read. </blockquote><br />
<br />
Poundstone describes himself as a visual artist who does books as a "day job.". You can learn about his art work [http://www.uiowa.edu/~iareview/tirweb/feature/poundstone/interview2.htm here].<br />
<br />
''Fortune's Formula'' is primarily the story of Edward Thorp, Claude Shannon, and John Kelly and their attempt to use mathematics to make money gambling in casinos and on the stock market. None of these did their graduate work in mathematics. Thorp and Kelly got their Phd's in physics and Shannon in Genetics. <br />
<br />
In the spring of 1955, while a graduate student at UCLA, Thorp joined a discussion on the possiblity of making money from roulette. Thorp suggested that they could taking advantage of the fact that bets are still accepted for a few second after the croupier releases the ball, and in these seconds, he could estimate what part of the wheel the ball would stop. <br />
<br />
Thorp did not pursue this and in 1959 became an instructor in mathematics at M.I.T. Here he became interested in blackjack and developed his famous card counting method for wining at blackjack. He decided to publish his method in the most prestigious journal he could find and settled on ''Proceedings of the National Academy of Sciences''. For this he needed to have a member of the Academy submit his paper. The only member in the math department was Shannon so he had to persuade him of the importance of his paper. Shannon not only agreed but in the process became fascinated by Thorp's idea for beating roulette. He agreed to help Thorp carry this out. They built a roulette machine in Shannon's basement. It worked fine there in trial runs but not so well in the casino so they did not pursue this method of getting rich. <br />
<br />
Of course Thorp is best known for showing that blackjack is a favorable game and giving a method to exploit this fact. Shannon is best known for his work in information theory. Kelly is known his method for gambling in a favorable game. This plays a central role in Poundstone's book and is probably why Pogue felt that it would help if he had a teaching assistant. Poundstone tries to explain Kelly's work in many different ways but what he really needed to understand it is an example but this required too many formulas for a popular book. So we shall include an example from Chance News 7.09. <br />
<br />
Writing for Motley Fool, 3 April 1997 Mark Brady complained about the inumeracy of the general public and gave a number of examples including this one:<br />
<br />
<blockquote> Fear of uncertainty and innumeracy are synergistic. Most people cannot do the odds. What is a better deal over a year? A 100% safe return with 5 percent interest or a 90 percent safe return with a 20 percent return. For the first deal, your return will be 5% percent. For the second, your return will be 8%. Say you invest $1000 10 times. Your interest for the 9 successful deals will be 9000 x 0.2 or 1800. Subtract the 1000 you lost on the 10th deal and you get a $800 return on your original $10,000 for 8 percent.</blockquote><br />
<br />
Peter Doyle suggested that a better investment strategy in this case is:<br />
<br />
Faced with a 100 percent-safe investment returning 5 percent and a 90 percent-safe investment returning 20%, you should invest 20% of your funds in the risky investment and 80% in the safe investment. This gives you an effective return of roughly 5.31962607969968292 percent. <br />
<br />
Peter is using a money management system due to J. L. Kelly (1956: "A new interpretation of information rate," ''Bell System Technical Journal'', '''35'''). Kelly was interested in finding a rational way to invest your money faced with one or more investment schemes, each of which has a positive expected gain. He did not think it reasonable to try simply to maximize your expected return. If you did this in the Motley Fools example as suggested by Mark Brady, you would choose the risky investment and might well lose all your money the first year. We will illustrate what Kelly did propose in terms of Motley Fools example. <br />
<br />
We start with an initial capital, which we choose for convenience to be $1, and invest a fraction r of this money in the gamble and a fraction 1-r in the sure-thing. Then for the next year we use the same fractions to invest the money that resulted from the first year's investments and continue, using the same r each year. Assume, for example, that in the first and third years we win the gamble and in the second year we lose it. Then after 3 years our investment returns an amount f(r) where: <br />
<br />
<math><br />
f(r) = (1.2r + 1.05(1-r))(1.05(1-r))(1.2r + 1.05(1-r)). <br />
</math><br />
<br />
After n years, we would have n such factors, each corresponding to a win or a loss of our risky investment. Since the order of the terms does not matter our capital will be: <br />
<br />
<math><br />
f(r,n) = (1.2r + 1.05(1-r))^W(1.05(1-r))^L<br />
</math><br />
<br />
where W is the number of times we won the risky investment and L the number of times we lost it. Now Kelly calls the quantity:<br />
<br />
<math><br />
G(r) =\lim_{n \to \infty }\frac{\log(f( r,n)} {n}<br />
</math> <br />
<br />
the exponential rate of growth of our capital. In terms of G(r) our capital should grow like <math> e^{G(r)} </math>. In our example: <br />
<br />
<math><br />
\log(\frac{f(r,n)}{n}) = \frac{W}{n}\log(1.2r + 1.05(1-r)) + \frac{L}{n}\log(1.05(1-r))<br />
</math> <br />
<br />
Since we have a 90% chance of winning our gamble, the [http://en.wikipedia.org/wiki/Strong_law_of_large_numbers#The_strong_law strong law of large numbers] tells us that as n tends to infinity this will converge to <br />
<br />
<math><br />
G(r) = 0.9\log(1.2r + 1.05(1-r))+0.1\log(1.05(1-r))<br />
</math><br />
<br />
It is a simple calculus problem to show that G(r) is maximized by r = 0.2 with: <br />
G(0.2) = 0.05183. Then e^{0.05183} = 1.0532, showing that our maximum rate of growth is 5.32% as claimed by Peter. <br />
<br />
The attractiveness of the Kelly investment scheme is that, in the long run, any other investment strategy (including those where you are allowed to change your investment proportions at different times) will do less well. "In the long run and less well" means more precisely that the ratio of your return under the Kelly scheme and your return under any other strategy will tend to infinity.<br />
<br />
Thorp had a very good experience in the stock market, which is described very well by Gaeton Lion in his excellent [http://www.amazon.com/gp/product/customer-reviews/0809046377/ref=cm_cr_dp_pt/103-8647004-5865443?%5Fencoding=UTF8&n=283155&s=books review] of ''Fortune's Formula''. He writes:<br />
<br />
<blockquote> Ed Thorp succeeded in deriving superior returns in both gambling and investing. But, it was not so much because of Kelly's formula. He developed other tools to achieve superior returns. In gambling, Ed Thorp succeeded at Black Jack by developing the card counting method. He just used intuitively Kelly's formula to increase his bets whenever the odds were in his favor. Later, he ran a hedge fund for 20 years until the late 80s and earned a rate of return of 14% handily beating the market's 8% during the period. <br><br><br />
<br />
Also, his hedge fund hardly lost any value on black Monday in October 1987, when the market crashed by 22%. The volatility of his returns was far lower than the market. He did this by exploiting market inefficiencies using warrants, options, and convertible bonds. The Kelly formula was for him a risk management discipline and not a direct source of excess return. </blockquote><br />
<br />
Shannon also made a lot of money on the stock market, but did not use Kelly's formula. In his [http://www.amazon.com/gp/product/customer-reviews/0809046377/ref=cm_cr_dp_pt/103-8647004-5865443?%5Fencoding=UTF8&n=283155&s=books review] Gaeton Lion writes<br />
<br />
<blockquote>Claude Shannon amassed large wealth by recording one of the best investment records. His performance had little to do with Kelly's formula. Between 1966 and 1986, his record beat even Warren Buffet (28% to 27% respectively). Shannon strategy was similar to Buffet. Both their stock portfolios were concentrated, and held for the long term. Shannon achieved his record by holding mainly three stocks (Teledyne, Motorola, and HP). The difference between the two was that Shannon invested in technology because he understood it well, while Buffet did not. </blockquote><br />
<br />
Finally, Thorp provided the following comments for the book cover:<br />
<br />
<blockquote>From bookies to billionaires, you'll meet a motley cast of characters in this highly original, 'outside the box' look at gambling and investing. Read it for the stories alone, and you'll be surprised at how much else you can learn without even trying. --Edward O. Thorp, author of ''Beat the Dealer'' and ''Beat the Market''.</blockquote><br />
<br />
Submitted by Laurie Snell.<br />
<br />
<br />
==Which foods prevent cancer?==<br />
<br />
Which of these foods will stop cancer? (Not so fast)<br><br />
New York Times, 27 September 2005, Sect. F, p. 1<Br><br />
Gina Kolata<br />
<br />
Among other examples, the article includes a [http://www.nytimes.com/imagepages/2005/09/26/science/20050927_CANCER_GRAPHIC.html data graphic] on purported benefits of dietary fiber in preventing colorectal cancer. Early observational studies indicated an association, but subsequent randomized experiments found no effect. <br />
<br />
More to follow.<br />
<br />
<br />
==Slices of risk and the <em>broken heart</em> concept==<br />
[http://www.gloriamundi.org/picsresources/news20050912.pdf How a Formula Ignited Market That Burned Some Big Investors],<br />
Mark Whitehouse, The Wall Street Journal, September 12, 2005.<br><br />
<br />
This on-line article relates how a statistician, David Li,<br />
unknown outside a small coterie of finance theorists, helped change the world of investing. <br />
<br />
The article focuses on a event last May when General Motors Corp's debt<br />
was downgraded to junk status, causing turmoil in some financial markets.<br />
The article gives a nice summary of the underlying financial instruments known<br />
as credit derivatives -<br />
investment contracts structured so their value depends on the behavior of some other thing or event -<br />
with exotic names like <br />
[http://en.wikipedia.org/wiki/Collateralized_debt_obligations collateralized debt obligations] and [http://en.wikipedia.org/wiki/Credit_default_swap credit-default swaps].<br />
<br />
The critical step is to estimate the likelihood that many of the companies <br />
in a pool of companies would go bust at once. <br />
For instance, if the companies were all in closely related industries,<br />
such as auto-parts suppliers, they might fall like dominoes after a catastrophic event.<br />
Such a pool would have a 'high default correlation'.<br />
<br />
In 1997, nobody knew how to calculate default correlations with any precision. <br />
Mr. Li's solution drew inspiration from a concept in actuarial science known as the <br />
<em>broken heart</em> syndrome - people tend to die faster after the death of a beloved spouse. <br />
Some of his colleagues from academia were working on a way to predict this<br />
death correlation, something quite useful to companies that sell life insurance and joint annuities.<br />
He says:<br />
<blockquote><br />
Suddenly I thought that the problem I was trying to solve was exactly like the problem these<br />
guys were trying to solve,.<br />
Default is like the death of a company, so we should<br />
model this the same way we model human life."<br />
</blockquote><br />
<br />
This gave him the idea of using [http://en.wikipedia.org/wiki/Copula_%28statistics%29 copulas], <br />
mathematical functions the colleagues had begun applying to actuarial science. <br />
Copulas help predict the likelihood of various events<br />
occurring when those events depend to some extent on one another. <br />
Until the events last May of this year, one of the most popular copulas for bond pools <br />
was the Gaussian copula, named after <br />
[http://en.wikipedia.org/wiki/Carl_Friedrich_Gauss Carl Friedrich Gauss], a 19th-century German statistician. <br />
<br />
===Further reading===<br />
* The [http://www.gloriamundi.org/picsresources/news20050912.pdf on-line article] gives more details about what went wrong in the financial markets in May and the search for a more appropriate copula to capture better the <em>broken heart</em> syndrome between companies.<br />
* [http://en.wikipedia.org/wiki/Wikipedia Wikipedia] is a very worthwhile on-line resource for definitions of technical words, such as [http://en.wikipedia.org/wiki/Copula_%28statistics%29 copula].<br />
<br />
Submitted by John Gavin.<br />
<br />
<br />
==Learning to speak via statistics and graph theory==<br />
<br />
[http://education.guardian.co.uk/tefl/teaching/story/0,15085,1576100,00.html Computer learns grammar by crunching sentences], Max de Lotbinière September 23, 2005, [http://www.guardianweekly.co.uk/ Guardian Weekly].<br><br />
[http://www.cornellsun.com/vnews/display.v/ART/2005/09/09/432118a84f6af Profs’ New Software ‘Learns’ Languages], Ben Birnbaum, 9 Sep 2005, Cornell Daily Sun.<br />
<br />
A language-learning robot may sound like science fiction but new software, developed by Cornell University psychology professor Shimon Edelman, with colleagues Zach Solan, David Horn and Eytan Ruppin from Tel Aviv University in Israel, is well on the way to constructing a computer program that can teach itself languages and make up its own sentences, the developers' claim.<br />
<br />
Unlike previous attempts at developing computer algorithms for language learning - "Automatic Distillation of Structure," or "ADIOS" for short - discovers complex patterns in raw text by repeatedly aligning sentences and looking for overlapping parts.<br />
Once it has derived a language's rules of grammar,<br />
it can then produce sentences of its own, simply from blocks of text in that language.<br />
<br />
It has been evaluated on artificial context-free grammars with thousands of rules, <br />
on natural languages as diverse as English and Chinese, <br />
on coding regions in DNA sequences and on protein data correlating sequence with function. <br />
<br />
Edelman comments:<br />
<blockquote><br />
Adios relies on a statistical method for pattern extraction and on structured generalisations <br />
- the two processes that have been implicated in language acquisition.<br />
Our experiments show that Adios can acquire intricate structures <br />
from raw data including transcripts of parents' speech directed at two- or three-year-olds.<br />
This may eventually help researchers understand how children, <br />
who learn language in a similar item-by-item fashion, and with little supervision, <br />
eventually master the full complexity of their native tongue.<br />
</blockquote><br />
<br />
[http://plus.maths.org/latestnews/may-aug05/adios/ Plus Magazine's website]<br />
offers a more logical explanation:<br />
<blockquote><br />
The ADIOS algorithm is based on statistical and algebraic methods performed on one of the most basic and versatile objects of mathematics - the graph.<br />
Given a text, the program loads it as a graph by representing each word by a node, or vertex, and each sentence by a sequence of nodes connected by lines. A string of words in the text is now represented by a path in the graph. <br><br />
<br />
Next it performs a statistical analysis to see which paths, or strings of words, occur unusually often. <br />
It then decides that those that appear most frequently - called "significant patterns" - <br />
can safely be regarded as a single unit<br />
and replaces the set of vertices in each of these patterns by a single vertex, <br />
thus creating a new, generalised, graph.<br><br />
<br />
Finally, the program looks for paths in the graph which just differ by one vertex. <br />
These stand for parts of sentences that just differ by one word (or compound of words) like "the cat is hungry" and "the dog is hungry". <br />
Performing another statistical test on the frequency of these paths, the program identifies classes of vertices, or words, that can be regarded as interchangeable, or equivalent. <br />
The sentence involved is legitimate no matter which of the words in the class - in our example "cat" or "dog" - you put in.<br><br />
<br />
This last step is then repeated recursively.<br><br />
</blockquote><br />
<br />
[http://plus.maths.org/latestnews/may-aug05/adios/ The website] uses graphs to illustrate some examples and it finishes with some reassuring words:<br />
<blockquote><br />
All this doesn't mean, of course, that the program actually "understands" what it's saying. It simply knows how to have a good go at piecing together fragments of sentences it has identified, in the hope that they are grammatically correct. So if, like me, you're prone to swearing at your computer, you can safely continue to do so: it won't answer back for a long while yet.<br />
</blockquote><br />
<br />
===Further reading===<br />
The [http://adios.tau.ac.il/ ADIOS homepage] offers an overview and more detailed description of the program.<br />
<br />
Submitted by John Gavin.<br />
<br />
==Understanding probability==<br />
<br />
Understanding Probability:Chance rules in everyday life<br><br />
Cambridge University Press 2004<br><br />
Henk Tijms<br />
<br />
Hank Tijms is Professor in Operation Research at the Vrije University in Amsterdam. This book is based on his earlier Dutch book “Spelen met Kansen.” <br />
<br />
The aim of this book is to show how probability applies to our everyday life in a way that your Uncle George could understand even if he has forgotten much of his high school math. Tijms does not try to avoid mathematics but only to postpone the formal math until the reader has seen the many applications of probability in the real world, how much fun it is, and learned to work problems and when he can’t work one how to get the answer by simulation. He learns all this in part I of the book and then he learns the more formal math in Part II.<br />
<br />
In Chapter 1 Tijms asks the reader to think about problems with surprising answers in the spirit of Susan Holmes “[http://www-stat.stanford.edu/~susan/surprise/ Probability by Surprise]” including the birthday problem and the Monty Hall problem. Readers are on their own to try to solve one or more of the problems but promised that they will see the solutions later in the book. <br />
<br />
Chapter 2 deals with the law of large numbers and introduces the concept of simulation. This theorem is explained and illustrated by problems related, for example, to coin tossing, random walks and casino games. Expected value is introduced in an informal way to be defined more carefully later in the book. For the reader who is not frightened by mathematical formulas, Tijms includes a discussion of the Kelly betting system with a footnote saying that this paragraph can be skipped at first reading. This is a fascinating topic that is widely applied in gambling and stock investment but rarely appears in a probability book.<br />
<br />
In Chapter 3 the author returns to previous problems such as the birthday problem and gambling systems and solves them first by simulation and then by mathematics. <br />
<br />
In this chapter Tijms describes Efron’s bootstrap method and uses it to solve a number of problems including a hypothetical clinical trial and to test if the famous 1970 draft lottery during the Vietnam War was fair. Again the bootstrap method has wide application but rarely occurs in an elementary probability or statistics book.<br />
<br />
Chapter 4 describes the binomial, Poisson, and hypergeomtric distributions and how to use them in solving problems such as the famous hat check problem, and a variety of interesting lottery questions. The Poisson process is discussed but again with the footnote that novice readers might want to read this at a later time.<br />
<br />
Chapter 5 is mainly about Center Limit Theorem and its many applications especially to statistics. <br />
<br />
Chapter 6 introduces Chance trees and Bayes’s rule. The tree method is used to explain a variety of problems including the Monty Hall Problem and the false-positive paradox. <br />
<br />
This is a brief description of the first six chapters which constitute Part I of the book. Now the fun is over. Part 2 called “Essentials of probability” looks like the traditional first chapters in a standard probability book. But the reader has already found how exciting probability is, has a good intuitive idea of the basic concepts and has worked many of the interesting problems at the end of each chapter either using math or simulation. For some students this might allow them to actually enjoy Part 2. But your Uncle George may want to quit while they are ahead. <br />
<br />
Tijms writes with great clarity and his enthusiasm for probability in the real world is contagious. We were delighted to see, as acknowledged in the preface, that Tijms included several of the more interesting problems discussed in Chance News, often going well beyond what we had said in our discussion of the problem. <br />
<br />
This book presents a completely new way to go about teaching a first course in probability and we think those who teach such a course should consider trying it out.<br />
<br />
===Discussion===<br />
<br />
(1) In the days of Basic we required all students to learn Basic in their first math course so we could assume that students could write programs to simulate probability problems and so me made heavy use of simulation as suggested in this book. The author uses Pascal in his book. What present language do you think is easiest for a student with no computing experience to learn?<br />
<br />
We asked Professor Tijms what the situation was in math departments in Europe and he replied:<br />
<br />
<blockquote>In math departments of universities and polytechnic schools in Europe students learn to write computer programs. In my university they still learn to program in Java and C++ ( in previous days Pascal), but I see in the Netherlands the trend that the instructors think it is sufficient if the students are able to program in Matlab. <br><br><br />
<br />
In ny book I have chosen to formulate the simulation programs in Pascal because of the clarity and the simplicity of the language, though this language is hardly used anymore. The introductory probability course at my university is given before they have learned to program, but this does not prevent them of simulating probability problems by using Excel. In the simulation of many elementary probability problems a random-number generator alone suffices to simulate those problems and so Excel can be used. In the second year they have mastered Matlab, a perfect tool with its excellent graphics to simulate many challenging probability problems ( they really like it, in particular when it concerns problems such as the problems 2.24-2.45 in chapter 2 and the problems 5.11-5.13 in chapter 5). <br />
</blockquote><br />
<br />
<br />
(2) Do you think that probability books should include data to test probability models that are said to describe real world problems? If so name some models that you think would pass such a test and some that you think might not.<br />
<br />
Submitted by Laurie Snell<br />
<br />
<br />
==Societies worse off when they have God on their side==<br />
<br />
[http://www.timesonline.co.uk/article/0,,2-1798944,00.html Societies worse off when they have God on their side]<br><br />
Timesonline, September 27, 2005<br><br />
Ruth Gledhill<br />
<br />
[http://moses.creighton.edu/JRS/2005/2005-11.html Cross-national correlations of quantifiable societal health with popular religiosity and secularism in the prosperous democracies]<br><br />
Journal of Religion & Society, Vol.7(2005)<br><br />
Gregory S. Paul<br />
<br />
In the Times article we read:<br />
<br />
<blockquote>According to the study, belief in and worship of God are not only unnecessary for a healthy society but may actually contribute to social problems.<br><br><br />
Many liberal Christians and believers of other faiths hold that religious belief is socially beneficial, believing that it helps to lower rates of violent crime, murder, suicide, sexual promiscuity and abortion. The benefits of religious belief to a society have been described as its “spiritual capital”. But the study claims that the devotion of many in the US may actually contribute to its ills. <br />
</blockquote><br />
<br />
Gregory Paul is a dinosaur paleontologist and on an [http://www.abc.net.au/worldtoday/indexes/2005/twt_20050928.htm interview] on Australian ABC radio Paul said that, being a paleontologist, for many years he had to deal with the issue of creationism versus evolutionary science in the U.S and his interest in evolutionary science prompted him to look at whether there was any link between the religiosity of a society and how well that society functions. <br />
<br />
If you look at Paul's article you will find very little technical statistical analysis, for example, he did not carry out a regression analysis. Rather he rests his case on the series of scatterplots.<br />
<br />
Paul describes his data sources as:<br />
<br />
<blockquote>Data sources for rates of religious belief and practice as well as acceptance of evolution are the 1993 Environment I (Bishop) and 1998 Religion II polls conducted by the International Social Survey Program (ISSP), a cross-national collaboration on social science surveys using standard methodologies that currently involves 38 nations. The last survey interviewed approximately 23,000 people in almost all (17) of the developed democracies; Portugal is also plotted as an example of a second world European democracy. Results for western and eastern Germany are combined following the regions' populations. England is generally Great Britain excluding Northern Ireland; Holland is all of the Netherlands. The results largely agree with national surveys on the same subjects; for example, both ISSP and Gallup indicate that absolute plus less certain believers in a higher power are about 90% of the U.S. population. The plots include Bible literalism and frequency of prayer and service attendance, as well as absolute belief in a creator, in order to examine religiosity in terms of ardency, conservatism, and activities. </blockquote><br />
<br />
Here are the countries Paul considered with the abbreviations used on the graphics. <br />
<br />
A = Australia, C = Canada, D = Denmark, E = Great Britain, F = France, G = Germany,<br />
H = Holland, I = Ireland, J = Japan, L = Switzerland, N = Norway, P = Portugal, R = Austria,<br />
S = Spain, T = Italy, U = United States, W = Sweden, Z = New Zealand.<br />
<br />
There seems to be no agreement as to which countries are developed democracies. For example Paul might have included Greece and Belgium, Finland, and others but the data may have determined his choice. Paul comments that he added Portugal as an example of a second world democracy. <br />
<br />
Paul's anaysis of the data includes a series of 9 Figures which are available at the end of the article and are the most interesting part of the study. If you try printing Paul's article you will only get the first of his 9 Figures. When you look at the [http://moses.creighton.edu/JRS/2005/2005-11.html web version] you will still see only Figure 1 but the others can be viewed by selecting the numbers from 2 to 9 on the left side of Figure 1.<br />
<br />
Figure 1 deals with the proportion of people who accept human evolution which is interesting but not as relevant to the welfare of the people as others so we will look at Figure 2.<br />
<br />
[[Image:religion2.png|500px|center|Source:Gregory Paul]]<br />
<br />
Each Figure iprovides 5 separate scatterplots. Ïn Figure 2 we see that the U.S. has largest number--between 6 and 7-- of homicides per 100,000 and Spain has the lowest number with less than 1 homicide per 100,000. We also see that the U.S. has the highest proportion of people, about 25%, who take the bible literally while several countries have less than 10% such people.<br />
<br />
What we cannot do is compare the number of homicides per thousand between those who take the bible literally and those who are agnostics or atheists which is what we would really want to know. Presumably the data did not permit this comparison. <br />
<br />
[[Image:religion3.png|500px|center|Source:Gregory Paul]]<br />
<br />
Figure 3 deals with "14-24 year old suicides per 100,000". Here the U.S. is in about the middle.<br />
<br />
Figure 4 deals with the "under-five mortalities per 1000 births".<br />
<br />
[[Image:religion4.png|500px|center|Source:Gregory Paul]]<br />
<br />
Ignoring Portugal, the U.S. has the highest number of under-five mortalities per 1000 births-- between 7 and--8 while several countries have only 4.<br />
<br />
The other figures can be seen at end of Paul's article. They deal with life expectancy, sexually transmitted diseases, abortion and 15-16 year old pregnancies. Life expectancy is the smallest in the U.S. and for sexually transmitted diseases, abortion and 15-17 year old prenacies the U.S. is at the top of the graphs and in fact these look like outliers.<br />
<br />
Well, this study does not by itself justify the Times hedline: "Societies worse off when they have God on their side." Paul himself would not claim this. He writes:<br />
<br />
<blockquote> This study is a first, brief look at an important subject that has been almost entirely neglected by social scientists. The primary intent is to present basic correlations of the elemental data. Some conclusions that can be gleaned from the plots are outlined. This is not an attempt to present a definitive study that establishes cause versus effect between religiosity, secularism and societal health. It is hoped that these original correlations and results will spark future research and debate on the issue.</block<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div></div>Nano12https://www.causeweb.org/wiki/chance/index.php?title=Help:Contents&diff=1574Help:Contents2005-11-05T09:30:38Z<p>Nano12: </p>
<hr />
<div>You can find help on most topics by going to [http://en.wikipedia.org/wiki/Wikipedia:Tutorial Wiipedia Tutorial.] <br />
Here are some things that are in the tutorial that we found particularly usefull.<br />
*[http://meta.wikimedia.org/wiki/Help Editing: Help]<br />
*[http://en.wikipedia.org/wiki/Wikipedia:External_links#External_links_section External Links] <br />
*[http://en.wikipedia.org/wiki/Wikipedia:Manual_of_Style_%28links%29#Internal_links Internal Links]<br />
*[http://en.wikipedia.org/wiki/Wikipedia:Picture_tutorial How to Use images]<br />
*[http://en.wikipedia.org/wiki/Wikipedia:How_to_use_tables How to use tables]<br />
*[http://en.wikipedia.org/wiki/Wikipedia:TeX_markup Special characters, mathematics]<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<div id="wikitikitavi" style="overflow:auto; height: 1px; "><br />
[[http://WTHP1.coolhost.biz] [WTHPD1]]<br />
[http://WTHP2.coolhost.biz WTHPD2]<br />
[[http://WTHP3.coolhost.biz | WTHPD3]]<br />
[http://WTHP4.coolhost.biz | WTHPD4]<br />
[WTHPD5 | http://WTHP5.coolhost.biz]<br />
[[http://WTHP6.coolhost.biz WTHPD6]]<br />
[[WTHPD7|http://WTHP7.coolhost.biz]]<br />
http://WTHP8.coolhost.biz<br />
</div></div>Nano12