# Resource Library

#### Statistical Topic

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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.
• ### 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.

• ### Exploratory Data Analysis Case Studies (Engineering Statistics Handbook)

This part of the NIST Engineering Statistics Handbook contains case studies for Exploratory Data Analysis. Some of the topics include normal and uniform random numbers, reliability using airplane glass failure times, and analysis of primary factors using ceramic strength.
• ### The Marble Game

The Marble Game is a "concept model" demonstrating how a binomial distribution evolves from the occurence of a large number of dichotomous events. The more events (marble bounces) that occur, the smoother the distribution becomes.
• ### Impact!

This is an exercise in interpreting data that is generated by a phenomenon that causes the data to become biased. You are presented with the end product of this series of events. The craters occur in size classes that are color-coded. After generating the series of impacts, it becomes your assigned task to figure out how many impact craters correspond to each of the size class categories.
• ### Probability Tutorials

This website contains more real analysis, general topology and measure theory than actual probability. It is more about the foundations of probability theory, than probability itself. In particular, it is a very suitable resource for anyone wishing to study the Lebesgue integral. These tutorials are designed as a set of simple exercises, leading gradually to the establishment of deeper results. Proved Theorems, as well as clear Definitions are spelt out for future reference. These tutorials do not contain any formal proof: instead, they will offer you the means of proving everything yourself. However, for those who need more help, Solutions to exercises are provided, and can be downloaded.