There is an explosion of interest in Bayesian statistics, primarily because recently created computational methods have finally made Bayesian analysis tractable and accessible to a wide audience. Doing Bayesian Data Analysis, A Tutorial Introduction with R and BUGS, is for first year graduate students or advanced undergraduates and provides an accessible approach, as all mathematics is explained intuitively and with concrete examples. It assumes only algebra and ‘rusty’ calculus. Unlike other textbooks, this book begins with the basics, including essential concepts of probability and random sampling. The book gradually climbs all the way to advanced hierarchical modeling methods for realistic data. The text provides complete examples with the R programming language and BUGS software (both freeware), and begins with basic programming examples, working up gradually to complete programs for complex analyses and presentation graphics. These templates can be easily adapted for a large variety of students and their own research needs.The textbook bridges the students from their undergraduate training into modern Bayesian methods.
-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
First-year Graduate Students and Advanced Undergraduate Students in Statistics, Psychology, Cognitive Science, Social Sciences, Clinical Sciences and Consumer Sciences in Business.
1.) This Book’s Organization: Read Me First!
1.1 Real People Can Read This Book
1.3 The Organization of This Book
1.3.1 What Are the Essential Chapters?
1.3.2 Where’s the Equivalent of Traditional Test X in This Book
1.4 Gimme Feedback (Be Polite)
Part 1.) The Basics: Parameters, Probability, Bayes’ Rule, and R
2.) Introduction: Models We Believe In
2.1 Models of Observations and Models of Beliefs
2.1.1 Prior and Posterior Beliefs
2.2 Three Goals for Inference from Data
2.2.1 Estimation of Parameter Values
2.2.2 Prediction of Data Values
2.2.3 Model Comparison
2.3 The R Programming Language
2.3.1 Getting and Installing R
2.3.2 Invoking R and Using the Command Line
2.3.3 A Simple Example of R in Action
2.3.4 Getting Help in R
2.3.5 Programming in R
3.) What Is This Stuff Called Probability?
3.1 The Set of All Possible Events
3.1.1 Coin Flips: Why You Should Care
3.2 Probability: Outside or Inside the Head
3.2.1 Outside the Head: Long-Run Relative Frequency
3.2.2 Inside the Head: Subjective Belief
3.2.3 Probabilities Assign Numbers to Possibilities
3.3 Probability Distributions
3.3.1 Discrete Distributions: Probability Mass
3.3.2 Continuous Distributions: Rendezvous with Density
3.3.3 Mean and Variance of a Distribution
3.3.4 Variance as Uncertainty in Beliefs
3.3.5 Highest Density Interval (HDI)
3.4 Two-Way Distributions
3.4.1 Marginal Probability
3.4.2 Conditional Probability
3.4.3 Independence of Attributes
3.5 R Code
3.5.1 R Code for Figure 3.1
3.5.2 R Code for Figure 3.3
4.) Bayes’ Rule
4.1 Bayes’ Rule
4.1.1 Derived from Definitions of Conditional Probability
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John K. Kruschke is Professor of Psychological and Brain Sciences, and Adjunct Professor of Statistics, at Indiana University in Bloomington, Indiana, USA. He is eight-time 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 self-designed 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.
Indiana University, Bloomington, USA
"This book is head-and-shoulders better than the others I've seen. I'm using it myself right now. Here's what's good about it: •It builds from very simple foundations. •Math is minimized. No proofs. •From start to finish, everything is demonstrated through R programs. •It helps you learn Empirical Bayesian methods from every angle…"--Exploring Possibility Space blog, March 12, 2014