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  • Random Samples

    This online, interactive lesson on random samples provides examples, exercises, and applets concerning sample mean, law of large numbers, sample variance, partial sums, central limit theorem, special properties of normal samples, order statistics, and sample covariance and correlation.

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  • Point Estimation

    This online, interactive lesson on point estimation provides examples, exercises, and applets concerning estimators, method of moments, maximum likelihood, Bayes estimators, best unbiased estimators, and sufficient, complete and ancillary statistics.

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  • Markov Chains

    This online, interactive lesson on Markov chains provides examples, exercises, and applets that cover recurrence, transience, periodicity, time reversal, as well as invariant and limiting distributions.

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  • Resampling Statistics: Randomization and the Bootstrap

    This set of pages describes software the author wrote to implement bootstrap and resampling procedures. It also contains an introduction to resampling and the bootstrap; and examples applying these procedures to the mean, the median, correlation between two groups, and analysis of variance.

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  • Resampling methods: Concepts, Applications, and Justification

    This journal article is a summary of resampling methods such as the jackknife, bootstrap, and permutation tests. It summarizes the tests, describes various software to perform the tests, and has a list of references.

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  • 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.

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  • 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.

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  • 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.

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  • Sufficient Statistics

    This page introduces the definition of sufficient statistics and gives two examples of the use of factorization to prove sufficiency.

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  • Inference in Linear Regression

    This site gives an explanation, a definition and an example of inference in linear regression. Topics include confidence intervals for intercept and slope, significance tests, mean response, and prediction intervals.

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