Difference between revisions of "Chance News 58"

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(The remarkable story of Math's most contentious brain teaser.)
(The remarkable story of Math's most contentious brain teaser.)
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You make your decision. Monty now eliminates another goat-concealing door (at random) and once more gives you the choice either of sticking or switching.  This process continues until only two doors remain in play.  What strategy should you follow to maximize your chances of winning?
 
You make your decision. Monty now eliminates another goat-concealing door (at random) and once more gives you the choice either of sticking or switching.  This process continues until only two doors remain in play.  What strategy should you follow to maximize your chances of winning?
  
These versions of the Monty Hall problem that have led to fascinating mathematics problems have been solved by Jason and others. He describes some of these solutions in his book and gives many references for other. OF course the solution to version 1 (classical Monte) is well known. For version 2 (Bayesian Monty)  for n >= 4 the it has been proven that the optional strategy is to stick with your original door until only 2 doors remain and then switch, Your probability of winning is then (n-1)/n.  The proof is discussed in the book and also in
+
The different versions of the Monty Hall problem that have led to fascinating mathematics problems have been solved by Jason and others. He describes some of these solutions in his book and gives many references for other. OF course the solution to version 1 (classical Monte) is well known. For version 2 (Bayesian Monty)  for n >= 4, it has been proven that the optional strategy is to stick with your original door until only 2 doors remain and then switch, Your probability of winning is then (n-1)/n.  The proof is discussed in the book and also in
  
 
Optimal strategies for progressive Monty Hall Problems<br>  
 
Optimal strategies for progressive Monty Hall Problems<br>  

Revision as of 15:38, 6 December 2009

Quotations

Berkeley law professor Kevin Quinn is working on a "statistical time machine" to compare Supreme Court justices' positions across historical time periods. He emailed Carl Bialik ("Statistical Time Travel Helps Answer What-Ifs", The Wall Street Journal, November 12, 2009) the following quotation:

The famous statistician George Box once wrote that "all models are wrong, but some are useful."

Submitted by Margaret Cibes


Everyone believes in the normal law, the experimenters because they imagine that it is a mathematical theorem, and the mathematicians because they think it is an experimental fact.

Gabriel Lippmann (French physicist)
in Henri Poincaré's Calcul de probabilités, 1896

Submitted by Steve Simon


When times are good in financial markets, we’re willing to convince ourselves that they’re good for a reason. …. “When the trend is sideways to down, they think the machine is broken,” says [technical analyst] Robert Prechter. “Jeez, it can’t be us.”

….

Prechter readily admits that he’s far from infallible. The standard, he says he wants to be held to is similar to that of a hitter in baseball, in which batting .300 makes one a star and.400 an immortal.

“Riding the Waves,” TIME, November 30, 2009

Submitted by Margaret Cibes


From principles is derived probability, but truth or certainty is obtained only from facts.

Tom Stoppard

Submitted by Laurie Snell

Forsooth

These Forsooths are from the December 2009 RSSNews.

When to undertake surveys

The ideal time for monitoring walking
activity is when flows are highest, That is
usually in June, and is linked to good

weather and longer hours of daylight.
However, because most walk journeys are
for utility reasons, the number of walk
journeys per month does not vary greatly
- unlike cycling. School holidays influence
walking patterns and the purpose of a
trip is often time dependent.

It is uncertain to what extent the weather
influences the amount of walking activity
overall. It is likely that leisure walking is
more strongly affected by weather
conditions than walking for utility
purposes.

Department for Transport website
October 2009

40% rise in swine flu deaths in
48 hours as two more die
The number of swine flu deaths in
Scotland has soared by 40% in just 48
hours, after the Scottish Government
Confirmed last night that a further two
people died after contracting the virus.

The patients, a 48-year-old man from
Greater Glasgow and Clyde and an 81
- year-old Fife woman, were both carrying
the H1N1 strain

Their deaths take the total swine flu
fatalities to 14, marking a sudden increase
in the number of deaths since Glasgow
mother Jacqui Fletcher became the UK's
first swine flue victim in June.

GlasGow Herold
13 October 2009




In a Wall Street Journal article, "These Hobbyists Add to Calculators, Multiplying Their Fun", November 17, 2009, Dionne Searcey reports:

After two months of trying to crack the code - a process that involved factoring two huge prime numbers - Mr. Moody says he succeeded in July.

Submitted by Margaret Cibes


In a Psychology Today article, “Interacting with women makes men stupid”, May 18, 2009, Scott Barry Kaufman reports about a Dutch research paper, “Interacting with women can impair men’s cognitive functioning” (Journal of Experimental Social Psychology, May 2009).

The article’s author reports some Duh! results:

[M]ale participants tended to perform worse on a cognitive task …following the mixed-sex interaction compared to the same-sex interaction. …. Also, this effect was even stronger when the male participant reported higher attraction to the opposite-sex person they [sic] were interacting with. ….

It should be noted that there was evidence that women's cognitive performance did tend to decline after mixed-sex interactions if they reported having a relatively strong goal to impress the opposite-sex other.

The study is quoted as stating:

Part of boys' valuable cognitive resources may be spent on impressing their female class members.

Submitted by Margaret Cibes


In an Emax Health article, “Cell Phone Ringtones Can Impair Retention”, June 3, 2009, Kathleen Blanchard reports about an LSU study of the effect of cell phone ringtones on short-term information retention.

[P]eople exposed to cell phone ringtones had lower scores on tests after hearing ringtones in the classroom. ….
[The researcher] said the familiar LSU fight song… ”slowed down their decision-making performance for a longer time than even a standard ringtone."

See also “Cell phone ringtones can pose major distraction, impair recall”, by Gerry Everding, Washington University at St. Louis, May 28, 2009.

Submitted by Margaret Cibes

The value of negative data

Little Benefit Seen, So Far, in Electronic Patient Records, Steve Lohr, The New York Times, November 15, 2009.

Study Raises Questions About Cholesterol Drug’s Benefit, Natasha Singer, The New York Times, November 15, 2009.

Seeking a Shorter Path to New Drugs, Steve Lohr, The New York Times, November 15, 2009.

Negative data, data that disproves a commonly held belief about the superiority of a particular medical treatment, is especially valuable from an economic perspective, but doesn't get the respect it deserves.

Providing high tech electronic health records should lead to better care, but apparently it doesn't.

The nation is set to begin an ambitious program, backed by $19 billion in government incentives, to accelerate the adoption of computerized patient records in doctors’ offices and hospitals, replacing ink and paper. There is wide agreement that the conversion will bring better care and lower costs, saving the American health care system up to $100 billion a year by some estimates. But a new study comparing 3,000 hospitals at various stages in the adoption of computerized health records has found little difference in the cost and quality of care.

Previous studies had used a selected subset of health care practices.

The study is an unusual effort to measure the impact of electronic health records nationally. Most of the evidence for gains from the technology, Dr. Jha said, has come from looking at an elite group of large, high-performing health providers that have spent years adapting their practices to the technology. The group usually includes Kaiser Permanente, the Mayo Clinic, the Cleveland Clinic and Intermountain Healthcare, among others.

In another study, an expensive cholesterol lowering drug was found to perform less well than a simple inexpensive alternative.

For patients taking a statin to control high cholesterol, adding an old standby drug, niacin, was superior in reducing buildup in the carotid artery to adding Zetia, a newer drug that reduces bad cholesterol, according to a new study. The results of the study, published in The New England Journal of Medicine, were presented here Sunday night at an annual meeting of the American Heart Association.

The study was small (208 patients) and used a surrogate outcome, arterial wall thickness. The findings pitted raising good cholesterol against lowering bad cholesterol, and found that raising good cholesterol was better.

Over the course of the 14-month study, the bad cholesterol of the patients on Zetia decreased by 19.2 percent, but the patients’ arterial wall thickness stayed the same, the study said. In the niacin group, good cholesterol increased by 18.4 percent and the carotid wall thickness decreased.

But the use of arterial wall thickness also led to criticism by Dr. Peter S. Kim, the president of Merck Research Laboratories who said that

a drug’s ability to improve artery-wall thickness has not been proved to automatically correlate with a reduction in heart attacks.

The efficacy of Zetia has also been established on the basis of a surrogate outcome, reduction in levels of bad cholesterol.

Zetia, he said, lowers bad cholesterol and lowering bad cholesterol is a known good. The study results “should be compared to the overwhelming body of evidence that lowering LDL cholesterol is an important thing to do to improve cardiovascular health,” Dr. Kim said.

Others, however, felt that this study showed problems with a heavily marketed drug.

Some cardiologists here hailed the study as an indication that the popularity of Zetia and Vytorin, which had combined sales last year of about $4.6 billion, has far outstripped their evidence of a concrete benefit on heart health.

The final article noted the huge expense associated with drug development. Why does it cost $800 million to bring the average drug to market?

Most of the cost in drug development is the price of failure, said Mervyn Turner, the chief strategy officer at the drug giant Merck. This linear, trial-and-error method is no longer a sustainable model for big pharmaceutical companies. “We invest far too long in bad ideas,” Dr. Turner said in a phone interview. “It is really important to stop that at an earlier stage in the cycle.”

One of the suggestions to reduce drug development cost is to publicize early failures.

One idea is for drug makers to share information about compounds they have tried and shelved, for reasons like toxicity or inefficacy. Although many companies have committed to publishing the results of clinical trials, whether or not they succeed, drug makers don’t typically publish information about projects that fail at an earlier stage. A result is that companies waste many millions going down experimental paths that their competitors have already found to be dead ends.

Submitted by Steve Simon

Questions

1. Some people are trying to put a "spin" on the positive effects of electronic medical records at leading health care institutions and the lack of effect in a nationwide survey, as indicating that the electronic medical record works, but it takes time and effort. Do you agree or disagree?

2. Zetia was approved by the FDA on the basis of a surrogate outcome, reduction in bad cholesterol, rather than in an outcome like decreased mortality or reduction in the number of heart attacks. Should the FDA require a new drug to show effectiveness on a direct measure instead of a surrogate measure?

3. What are the barriers to drug companies sharing information about early failures in the drug development process?

Art for the birds

“A bird’s eye view of art”, Science News, June 30, 2009

According to this very brief article, Japanese Professor Shigeru Watanabe has published a study in Springer’s Animal Cognition, which concludes:

Pigeons could be art critics yet, ... like humans, pigeons can be trained to tell the difference between "good" and "bad" paintings.

Curious readers without access to this journal might be interested in an earlier, full-text online, Watanabe paper, “Pigeons’ Discrimination of Paintings by Monet and Picasso” (Journal of the Experimental Analysis of Behavior, March 1995).

Abstract: Pigeons successfully learned to discriminate color slides of paintings by Monet and Picasso. Following this training, they discriminated novel paintings by Monet and Picasso that had never been presented during the discrimination training. Furthermore, they showed generalization from Monet's to Cezanne's and Renoir's paintings or from Picasso's to Braque's and Matisse's paintings. These results suggest that pigeons' behavior can be controlled by complex visual stimuli in ways that suggest categorization. Upside-down images of Monet's paintings disrupted the discrimination, whereas inverted images of Picasso's did not. This result may indicate that the pigeons' behavior was controlled by objects depicted in impressionists'paintings but was not controlled by objects in cubists' paintings.

This paper describes in great detail (methodology, statistical test results) several controlled experiments on “eight experimentally naïve pigeons."

Submitted by Margaret Cibes

Diversification of stock portfolios

“More Stocks May Not Make a Portfolio Safer”
by Jason Zweig, The Wall Street Journal, November 26, 2009

Conventional wisdom among financial planners is that investing in 10 up to 30 or 40 stocks provides adequate diversification for risk reduction. This "wisdom" is apparently backed up by studies.

But this research on diversification was based on the average results of a large number of portfolios randomly generated by computer.

When LSU business professor Don Chance had his students build a portfolio of 30 stocks, one at a time, the results confirmed the conventional wisdom in that, after the first 20 stocks, portfolio risk, as measured by fluctuation in price, had been reduced by about 40% from that of the first stock alone.

However, when Chance analyzed his individual students’ portfolios, he found that increasing the portfolio size from the first stock to the 30th resulted in 11% of the portfolios having more fluctuation than their first choice and 23% having more fluctuation than their first 5 choices.

The lesson: For any given investor, the averages mightn't apply.

Chance found that his students had started their portfolios with a few brand-name companies with which they were familiar and soon ran out of familiar company names, subsequently picking stocks with much lower capitalization and thus more risk.

One financial planner commented:

Humans can't think randomly …. Once people think of Exxon Mobil, they're a lot more likely to think of Chevron or another oil stock. For a lot of investors, diversification is like doing a word-association game.

Another planner commented:

People who regard themselves as risk-averse will assemble portfolios of highly similar stocks that all seem to be "safe." The result, paradoxically, is a risky portfolio with every egg in one basket.

Chance also found that 13% of computer-generated 20-stock portfolios were riskier than one-stock portfolios.

See “Experimental Evidence on Portfolio Size and Diversification: Your Mileage May Vary” to download a copy of the report.

Submitted by Margaret Cibes

The remarkable story of Math's most contentious brain teaser.

The Monty Hall Problem Oxford Univerity Press, 2009
Jason Douglace Rosenhouse

Jason Graduated from Dartmouth in 2000 and is currently Associate Professor of Mathematics, at James Madison University, Harrisonburg Virginia. His research has been in number theory but here he has written a book on the Monty Hall problem.

Chapter 1 is called Ancestral Monty and includes among others a discussion of the Three Prisoners Paradox, Lets Make a Deal, and the Birth of the Monty Hall Problem. the Marylyn Vo Savant story that we all know about .

Chapter 2 is called Classical Monte. And described as follows

Version One: You are shown three identical doors. Behind one of them is a car. The other two conceal goats. You are asked to choose, but not open, one of the doors. After doing so, Monty, who knows where the car is, opens one of the two remaining doors. He always opens a door he knows to be incorrect, and randomly chooses which door to open when he has more than one option (Which happens on those occasions when your initial choice conceals the car). After opening an incorrect door, Monty gives you the choice of either switching to the unopened door or sticking with your original choice. You then receive what is in the door that you choose. What should you do?.

Chapter 3 is Bayesian Monty

This chapter considers this version.

Version Two: As before, Monty shows you three identical doors. One contains a car, the other two contain goats. You choose one of the doors but do not open it. This time, however, Monty does not know the location of the car. He randomly chooses one of the two doors different from your selection and opens it. The door turns out to conceal a goat. He now gives you the options either of sticking with your original door or switching to the other one. What should you do?

Jason shows how to solve these two versions explaining the mathematics used in the two solutions.


Chapter 4 is called Progressive Monty described as follows.

This time we assume there are n identical doors, where n is an integer satisfying n >=3. One door conceals a car, the other n-1 conceal goats. You choose one of the doors at random but do not open it. Monty then opens a door he knows to conceal a goat, always choosing randomly

always choosing randomly among the available doors. At this point he gives you the choice of sticking with your original door or switching to one of the remaining doors.

You make your decision. Monty now eliminates another goat-concealing door (at random) and once more gives you the choice either of sticking or switching. This process continues until only two doors remain in play. What strategy should you follow to maximize your chances of winning?

The different versions of the Monty Hall problem that have led to fascinating mathematics problems have been solved by Jason and others. He describes some of these solutions in his book and gives many references for other. OF course the solution to version 1 (classical Monte) is well known. For version 2 (Bayesian Monty) for n >= 4, it has been proven that the optional strategy is to stick with your original door until only 2 doors remain and then switch, Your probability of winning is then (n-1)/n. The proof is discussed in the book and also in

Optimal strategies for progressive Monty Hall Problems
The Mathematical Gazette
Vol 93 No 528, Page 410
November 2009
Steven K. Lucas, Jason Rosenhouse

You can find an earlier version by putting the title in google.

Submitted by Laurie Snell

Simpson’s Paradox in the news

“When Combined Data Reveal the Flaw of Averages”
by Cari Tuna, The Wall Street Journal, December 2, 2009

The subtitle of this article is “In a statistical Anomaly Dubbed Simpson’s Paradox, Aggregated Numbers Obscure Trends in Job Market, Medicine and Baseball.”

The author reports about an anomaly which results from comparing unemployment rates for two periods, the early 1980s recession period and the current 2009 period. While unemployment rates are now lower for the population of all adult Americans, the rates for some subgroups of the population are higher.

So how can the overall unemployment rate be lower today but higher among each group? The anomaly is an example of Simpson's Paradox -- a common but misleading statistical phenomenon rooted in the differing sizes of subgroups. Put simply, Simpson's Paradox reveals that aggregated data can appear to reverse important trends in the numbers being combined.

The author discusses the well known example of Berkeley’s 1973 graduate admissions data, a 1986 study of kidney-stone treatments, and baseball statistics.

[Harvard’s statistics chair] says he thinks many people who wield similarly misleading data do so unintentionally. "When you find data that go with your theory, then you don't dig deeper."

Bloggers [1] mentioned additional examples of Simpson’s Paradox, on topics such as mean SAT scores compared over time, and infant mortality rates compared among different countries.

On the ISOSTAT listserv, readers were referred to Andrew Gelman’s comments on this article in “Simpson’s Paradox not always such a paradox”, posted on his website, Statistical Modeling, Causal Inference, and Social Science, December 3, 2009.

Submitted by Margaret Cibes