Doing Bayesian Data Analysis
2nd Edition
A Tutorial with R, JAGS, and Stan
Description
Doing Bayesian Data Analysis: A Tutorial with R, JAGS, and Stan, Second Edition provides an accessible approach for conducting Bayesian data analysis, as material is explained clearly with concrete examples. Included are stepbystep instructions on how to carry out Bayesian data analyses in the popular and free software R and WinBugs, as well as new programs in JAGS and Stan. The new programs are designed to be much easier to use than the scripts in the first edition. In particular, there are now compact highlevel scripts that make it easy to run the programs on your own data sets.
The book is divided into three parts and begins with the basics: models, probability, Bayes’ rule, and the R programming language. The discussion then moves to the fundamentals applied to inferring a binomial probability, before concluding with chapters on the generalized linear model. Topics include metricpredicted variable on one or two groups; metricpredicted variable with one metric predictor; metricpredicted variable with multiple metric predictors; metricpredicted variable with one nominal predictor; and metricpredicted variable with multiple nominal predictors. The exercises found in the text have explicit purposes and guidelines for accomplishment.
This book is intended for firstyear graduate students or advanced undergraduates in statistics, data analysis, psychology, cognitive science, social sciences, clinical sciences, and consumer sciences in business.
Key Features
 Accessible, including the basics of essential concepts of probability and random sampling
 Examples with R programming language and JAGS software
 Comprehensive coverage of all scenarios addressed by nonBayesian textbooks: ttests, analysis of variance (ANOVA) and comparisons in ANOVA, multiple regression, and chisquare (contingency table analysis)
 Coverage of experiment planning
 R and JAGS computer programming code on website
 Exercises have explicit purposes and guidelines for accomplishment

Provides stepbystep instructions on how to conduct Bayesian data analyses in the popular and free software R and WinBugs
Readership
Firstyear Graduate Students and Advanced Undergraduate Students in Statistics, Data Analysis, Psychology, Cognitive Science, Social Sciences, Clinical Sciences and Consumer Sciences in Business.
Table of Contents
Chapter 1: What's in This Book (Read This First!)
 1.1 Real people can read this book
 1.2 What's in this book
 1.3 What's new in the second edition?
 1.4 Gimme feedback (Be polite)
 1.5 Thank you!
Part I: The Basics: Models, Probability, Bayes’ Rule, and R
Introduction
Chapter 2: Introduction: Credibility, Models, and Parameters
 2.1 Bayesian inference is reallocation of credibility across possibilities
 2.2 Possibilities are parameter values in descriptive models
 2.3 The steps of bayesian data analysis
 2.4 Exercises
Chapter 3: The R Programming Language
 3.1 Get the software
 3.2 A simple example of R in action
 3.3 Basic commands and operators in R
 3.4 Variable types
 3.5 Loading and saving data
 3.6 Some utility functions
 3.7 Programming in R
 3.8 Graphical plots: Opening and saving
 3.9 Conclusion
 3.10 Exercises
Chapter 4: What is This Stuff Called Probability?
 4.1 The set of all possible events
 4.2 Probability: Outside or inside the head
 4.3 Probability distributions
 4.4 Twoway distributions
 4.5 Appendix: R code for figure 4.1
 4.6 Exercises
Chapter 5: Bayes' Rule
 5.1 Bayes' rule
 5.2 Applied to parameters and data
 5.3 Complete examples: Estimating bias in a coin
 5.4 Why bayesian inference can be difficult
 5.5 Appendix: R code for figures 5.1, 5.2, etc.
 5.6 Exercises
Part II: All the Fundamentals Applied to Inferring a Binomial Probability
Introduction
Chapter 6: Inferring a Binomial Probability via Exact Mathematical Analysis
 6.1 The likelihood function: Bernoulli distribution
 6.2 A description of credibilities: The beta distribution
 6.3 The posterior beta
 6.4 Examples
 6.5 Summary
 6.6 Appendix: R code for figure 6.4
 6.7 Exercises
Chapter 7: Markov Chain Monte Carlo
 7.1 Approximating a distribution with a large sample
 7.2 A simple case of the metropolis algorithm
 7.3 The metropolis algorithm more generally
 7.4 Toward gibbs sampling: Estimating two coin biases
 7.5 Mcmc representativeness, accuracy, and efficiency
 7.6 Summary
 7.7 Exercises
Chapter 8: JAGS
 8.1 Jags and its relation to R
 8.2 A complete example
 8.3 Simplified scripts for frequently used analyses
 8.4 Example: difference of biases
 8.5 Sampling from the prior distribution in jags
 8.6 Probability distributions available in jags
 8.7 Faster sampling with parallel processing in runjags
 8.8 Tips for expanding jags models
 8.9 Exercises
Chapter 9: Hierarchical Models
 9.1 A single coin from a single mint
 9.2 Multiple coins from a single mint
 9.3 Shrinkage in hierarchical models
 9.4 Speeding up jags
 9.5 Extending the hierarchy: Subjects within categories
 9.6 Exercises
Chapter 10: Model Comparison and Hierarchical Modeling
 10.1 General formula and the bayes factor
 10.2 Example: two factories of coins
 10.3 Solution by MCMC
 10.4 Prediction: Model averaging
 10.5 Model complexity naturally accounted for
 10.6 Extreme sensitivity to prior distribution
 10.7 Exercises
Chapter 11: Null Hypothesis Significance Testing
 11.1 Paved with good intentions
 11.2 Prior knowledge
 11.3 Confidence interval and highest density interval
 11.4 Multiple comparisons
 11.5 What a sampling distribution is good for
 11.6 Exercises
Chapter 12: Bayesian Approaches to Testing a Point (“Null”) Hypothesis
 12.1 The estimation approach
 12.2 The modelcomparison approach
 12.3 Relations of parameter estimation and model comparison
 12.4. Estimation or model comparison?
 12.5. Exercises
Chapter 13: Goals, Power, and Sample Size
 13.1 The will to power
 13.2 Computing power and sample size
 13.3 Sequential testing and the goal of precision
 13.4 Discussion
 13.5 Exercises
Chapter 14: Stan
 14.1 HMC sampling
 14.2 Installing stan
 14.3 A complete example
 14.4 Specify models topdown in stan
 14.5 Limitations and extras
 14.6 Exercises
Part III: The Generalized Linear Model
Introduction
Chapter 15: Overview of the Generalized Linear Model
 15.1 Types of variables
 15.2 Linear combination of predictors
 15.3 Linking from combined predictors to noisy predicted data
 15.4 Formal expression of the GLM
 15.5 Exercises
Chapter 16: MetricPredicted Variable on One or Two Groups
 16.1 Estimating the mean and standard deviation of a normal distribution
 16.2 Outliers and robust estimation: The t distribution
 16.3 Two groups
 16.4 Other noise distributions and transforming data
 16.5 Exercises
Chapter 17: Metric Predicted Variable with One Metric Predictor
 17.1 Simple linear regression
 17.2 Robust linear regression
 17.3 Hierarchical regression on individuals within groups
 17.4 Quadratic trend and weighted data
 17.5 Procedure and perils for expanding a model
 17.6 Exercises
Chapter 18: Metric Predicted Variable with Multiple Metric Predictors
 18.1 Multiple linear regression
 18.2 Multiplicative interaction of metric predictors
 18.3 Shrinkage of regression coefficients
 18.4 Variable selection
 18.5 Exercises
Chapter 19: Metric Predicted Variable with One Nominal Predictor
 19.1 Describing multiple groups of metric data
 19.2 Traditional analysis of variance
 19.3 Hierarchical bayesian approach
 19.4 Including a metric predictor
 19.5 Heterogeneous variances and robustness against outliers
 19.6 Exercises
Chapter 20: Metric Predicted Variable with Multiple Nominal Predictors
 20.1 Describing groups of metric data with multiple nominal predictors
 20.2 Hierarchical bayesian approach
 20.3 Rescaling can change interactions, homogeneity, and normality
 20.4 Heterogeneous variances and robustness against outliers
 20.5 Withinsubject designs
 20.6 Model comparison approach
 20.7 Exercises
Chapter 21: Dichotomous Predicted Variable
 21.1 Multiple metric predictors
 21.2 Interpreting the regression coefficients
 21.3 Robust logistic regression
 21.4 Nominal predictors
 21.5 Exercises
Chapter 22: Nominal Predicted Variable
 22.1 Softmax regression
 22.2 Conditional logistic regression
 22.3 Implementation in jags
 22.4 Generalizations and variations of the models
 22.5 Exercises
Chapter 23: Ordinal Predicted Variable
 23.1 Modeling ordinal data with an underlying metric variable
 23.2 The case of a single group
 23.3 The case of two groups
 23.4 The case of metric predictors
 23.5 Posterior prediction
 23.6 Generalizations and extensions
 23.7 Exercises
Chapter 24: Count Predicted Variable
 24.1 Poisson exponential model
 24.2 Example: hair eye go again
 24.3 Example: interaction contrasts, shrinkage, and omnibus test
 24.4 Loglinear models for contingency tables
 24.5 Exercises
Chapter 25: Tools in the Trunk
 25.1 Reporting a bayesian analysis
 25.2 Functions for computing highest density intervals
 25.3 Reparameterization
 25.4 Censored data in JAGS
 25.5 What next?
Details
 No. of pages:
 776
 Language:
 English
 Copyright:
 © Academic Press 2015
 Published:
 3rd November 2014
 Imprint:
 Academic Press
 Hardcover ISBN:
 9780124058880
 eBook ISBN:
 9780124059160
About the Author
John Kruschke
John K. Kruschke is Professor of Psychological and Brain Sciences, and Adjunct Professor of Statistics, at Indiana University in Bloomington, Indiana, USA. He is eighttime winner of Teaching Excellence Recognition Awards from Indiana University. He won the Troland Research Award from the National Academy of Sciences (USA), and the Remak Distinguished Scholar Award from Indiana University. He has been on the editorial boards of various scientific journals, including Psychological Review, the Journal of Experimental Psychology: General, and the Journal of Mathematical Psychology, among others.
After attending the Summer Science Program as a high school student and considering a career in astronomy, Kruschke earned a bachelor's degree in mathematics (with high distinction in general scholarship) from the University of California at Berkeley. As an undergraduate, Kruschke taught selfdesigned tutoring sessions for many math courses at the Student Learning Center. During graduate school he attended the 1988 Connectionist Models Summer School, and earned a doctorate in psychology also from U.C. Berkeley. He joined the faculty of Indiana University in 1989. Professor Kruschke's publications can be found at his Google Scholar page. His current research interests focus on moral psychology.
Professor Kruschke taught traditional statistical methods for many years until reaching a point, circa 2003, when he could no longer teach corrections for multiple comparisons with a clear conscience. The perils of p values provoked him to find a better way, and after only several thousand hours of relentless effort, the 1st and 2nd editions of Doing Bayesian Data Analysis emerged.
Affiliations and Expertise
Indiana University, Bloomington, USA
Reviews
"Both textbook and practical guide, this work is an accessible account of Bayesian data analysis starting from the basics…This edition is truly an expanded work and includes all new programs in JAGS and Stan designed to be easier to use than the scripts of the first edition, including when running the programs on your own data sets." MAA Reviews, Doing Bayesian Data Analysis, Second Edition
“fills a gaping hole in what is currently available, and will serve to create its own market” Prof. Michael Lee, U. of Cal., Irvine; pres. Society for Mathematical Psych.
“has the potential to change the way most cognitive scientists and experimental psychologists approach the planning and analysis of their experiments" Prof. Geoffrey Iverson, U. of Cal., Irvine; past pres. Society for Mathematical Psych.
“better than others for reasons stylistic.... buy it  it’s truly amazin’!” James L. (Jay) McClelland, Lucie Stern Prof. & Chair, Dept. of Psych., Stanford U.
"the best introductory textbook on Bayesian MCMC techniques" J. of Mathematical Psych.
"potential to change the methodological toolbox of a new generation of social scientists" J. of Economic Psych.
"revolutionary" British J. of Mathematical and Statistical Psych.
"writing for real people with real data. From the very first chapter, the engaging writing style will get readers excited about this topic" PsycCritiques