# Calculus required

• ### BGIM : Maximum Likelihood Estimation Primer

This set of pages is an introduction to Maximum Likelihood Estimation. It discusses the likelihood and log-likelihood functions and the process of optimizing.
• ### Belief in the Law of Small Numbers

This journal article gives examples of erroneous beliefs about probability. It specifically examines the belief that a random sample must be representative of the true population.
• ### Teaching Bayesian Reasoning in Less Than Two Hours

This journal article describes a set of experiments in which different methods of teaching Bayes' Theorem were compared to each other. The frequency representation of the rule was found to be easier to learn than the probability representation.
• ### Sufficient Statistics

This page introduces the definition of sufficient statistics and gives two examples of the use of factorization to prove sufficiency.
• ### Analysis Tool: Empirical Distributions

This applet plots the survival function (1-F(t)) of the exponential distribution against the empirical survival function. The empirical survival function is one minus the empirical distribution function.

• ### The Cramer-Rao Lower Bound

This page introduces the Cramer-Rao lower bound, discusses it's usefulness, and proves the inequality.
• ### Cramer-Rao Lower Bound: an Example

This file applies the Cramer-Rao inequality to a binomial random variable to prove that the usual estimator of p is a minimum variance unbiased estimator.
• ### Statistical Inference

This page contains course notes and homework assignments with solutions for a mathematical statistics class. The course covers statistical inference, probability, and estimation principles.
• ### Properties of an Estimator

These slides address point estimation including unbiasedness and efficiency and the Cramer-Rao lower bound.
• ### Theoretical Underpinnings of the Bootstrap

This page discusses the theory behind the bootstrap. It discusses the empirical distribution function as an approximation of the distribution function. It also introduces the parametric bootstrap.