Winner of the 2016 De Groot Prize from the International Society for Bayesian Analysis
Now in its third edition, this classic book is widely considered the leading text on Bayesian methods, lauded for its accessible, practical approach to analyzing data and solving research problems. Bayesian Data Analysis, Third Edition continues to take an applied approach to analysis using up-to-date Bayesian methods. The authors—all leaders in the statistics community—introduce basic concepts from a data-analytic perspective before presenting advanced methods. Throughout the text, numerous worked examples drawn from real applications and research emphasize the use of Bayesian inference in practice.
New to the Third Edition
- Four new chapters on nonparametric modeling
- Coverage of weakly informative priors and boundary-avoiding priors
- Updated discussion of cross-validation and predictive information criteria
- Improved convergence monitoring and effective sample size calculations for iterative simulation
- Presentations of Hamiltonian Monte Carlo, variational Bayes, and expectation propagation
- New and revised software code
The book can be used in three different ways. For undergraduate students, it introduces Bayesian inference starting from first principles. For graduate students, the text presents effective current approaches to Bayesian modeling and computation in statistics and related fields. For researchers, it provides an assortment of Bayesian methods in applied statistics. Additional materials, including data sets used in the examples, solutions to selected exercises, and software instructions, are available on the book’s web page.
Table of Contents
FUNDAMENTALS OF BAYESIAN INFERENCE
Probability and Inference
Introduction to Multiparameter Models
Asymptotics and Connections to Non-Bayesian Approaches
FUNDAMENTALS OF BAYESIAN DATA ANALYSIS
Evaluating, Comparing, and Expanding Models
Modeling Accounting for Data Collection
Introduction to Bayesian Computation
Basics of Markov Chain Simulation
Computationally Efficient Markov Chain Simulation
Modal and Distributional Approximations
Introduction to Regression Models
Hierarchical Linear Models
Generalized Linear Models
Models for Robust Inference
Models for Missing Data
NONLINEAR AND NONPARAMETRIC MODELS
Parametric Nonlinear Models
Basic Function Models
Gaussian Process Models
Finite Mixture Models
Dirichlet Process Models
A: Standard Probability Distributions
B: Outline of Proofs of Asymptotic Theorems
C: Computation in R and Stan
Bibliographic Notes and Exercises appear at the end of each chapter.
"The second edition was reviewed in JASA by Maiti (2004) … we now stand 10 years later with an even more impressive textbook that truly stands for what Bayesian data analysis should be. … this being a third edition begets the question of what is new when compared with the second edition? Quite a lot … this is truly the reference book for a graduate course on Bayesian statistics and not only Bayesian data analysis."
—Christian P. Robert, Journal of the American Statistical Association, September 2014, Vol. 109
Praise for the Second Edition
… it is simply the best all-around modern book focused on data analysis currently available. … There is enough important additional material here that those with the first edition should seriously consider updating to the new version. … when students or colleagues ask me which book they need to start with in order to take them as far as possible down the road toward analyzing their own data, Gelman et al. has been my answer since 1995. The second edition makes this an even more robust choice.
—Lawrence Joseph, Montreal General Hospital and McGill University, Statistics in Medicine, Vol. 23, 2004
I am thoroughly excited to have this book in hand to supplement course material and to offer research collaborators and clients at our consulting lab more sophisticated methods to solve their research problems.
—John Grego, University of South Carolina, USA
… easily the most comprehensive, scholarly, and thoughtful book on the subject, and I think will do much to promote the use of Bayesian methods
—David Blackwell, University of California, Berkeley, USA