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Doing Bayesian Data Analysis: A Tutorial with R and BUGS

There is an explosion of interest in Bayesian statistics, primarily because recently created computational methods have finally made Bayesian analysis obtainable to a wide audience. Doing Bayesian Data Analysis, A Tutorial Introduction with R and BUGS provides an accessible approach to Bayesian data analysis, as material is explained clearly with concrete examples. The book begins with the basics, including essential concepts of probability and random sampling, and gradually progresses to advanced hierarchical modeling methods for realistic data. The text delivers comprehensive coverage of all scenarios addressed by non-Bayesian textbooks--t-tests, analysis of variance (ANOVA) and comparisons in ANOVA, multiple regression, and chi-square (contingency table analysis).
This book is intended for first year graduate students or advanced undergraduates. It provides a bridge between undergraduate training and modern Bayesian methods for data analysis, which is becoming the accepted research standard. Prerequisite is knowledge of algebra and basic calculus.
Author website: http://www.indiana.edu/~kruschke/DoingBayesianDataAnalysis/
-Accessible, including the basics of essential concepts of probability and random sampling
-Examples with R programming language and BUGS software
-Comprehensive coverage of all scenarios addressed by non-bayesian textbooks- t-tests, analysis of variance (ANOVA) and comparisons in ANOVA, multiple regression, and chi-square (contingency table analysis).
-Coverage of experiment planning
-R and BUGS computer programming code on website
-Exercises have explicit purposes and guidelines for accomplishment

Output of a Bayesian graph segmentation algorithm on the "high resolution" 2000 US Census commuter dataset for Pennsylvania. The algorithm clusters economically related municipalities by joining together places with lots of commuter traffic between them.

Without prior knowledge of the number of clusters, the algorithm does a decent job of identifying economically linked regions around Philadelphia, Pittsburgh, Erie, Harrisburg, Wilks-Barre, and Scranton, among others. In sparser areas, the algorithm's partitions of the state match county lines---proposing in effect that people who live in rural counties tend to work in those counties. This despite the fact that input data contains no information about counties: it's simply a matrix of how many people commute to work between municipality A and municipality B.

An example Bayesian network and their relevance to artificial intelligence in the context of games.

Aliens affect bad weather. Zombies affect delivery. Bad weather and delivery affect whether we get a pizza in 45 minutes or not.

This probably isn't that amusing unless you're a computer scientist with a penchant for absurdities.

Praise for the First Edition
"I cannot think of a better book for teachers of introductory statistics who want a readable and pedagogically sound text to introduce Bayesian statistics."
—Statistics in Medical Research
"[This book] is written in a lucid conversational style, which is so rare in mathematical writings. It does an excellent job of presenting Bayesian statistics as a perfectly reasonable approach to elementary problems in statistics."
—STATS: The Magazine for Students of Statistics, American Statistical Association
"Bolstad offers clear explanations of every concept and method making the book accessible and valuable to undergraduate and graduate students alike."
—Journal of Applied Statistics
The use of Bayesian methods in applied statistical analysis has become increasingly popular, yet most introductory statistics texts continue to only present the subject using frequentist methods. Introduction to Bayesian Statistics, Second Edition focuses on Bayesian methods that can be used for inference, and it also addresses how these methods compare favorably with frequentist alternatives. Teaching statistics from the Bayesian perspective allows for direct probability statements about parameters, and this approach is now more relevant than ever due to computer programs that allow practitioners to work on problems that contain many parameters.
This book uniquely covers the topics typically found in an introductory statistics book—but from a Bayesian perspective—giving readers an advantage as they enter fields where statistics is used. This Second Edition provides:
Extended coverage of Poisson and Gamma distributions
Two new chapters on Bayesian inference for Poisson observations and Bayesian inference for the standard deviation for normal observations
A twenty-five percent increase in exercises with selected answers at the end of the book
A calculus refresher appendix and a summary on the use of statistical tables
New computer exercises that use R functions and Minitab® macros for Bayesian analysis and Monte Carlo simulations
Introduction to Bayesian Statistics, Second Edition is an invaluable textbook for advanced undergraduate and graduate-level statistics courses as well as a practical reference for statisticians who require a working knowledge of Bayesian statistics.

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