Gelman Andrew, Carlin John B., Stern Hal S., Rubin Donald B. Bayesian Data Analysis

Second Edition. — Chapman & Hall/CRC, 2004. — (Тexts in Statistical Science).Incorporating new and updated information, this second edition of THE bestselling text in Bayesian data analysis continues to emphasize practice over theory, describing how to conceptualize, perform, and critique statistical analyses from a Bayesian perspective. Its world-class authors provide guidance on all aspects of Bayesian data analysis and include examples of real statistical analyses, based on their own research, that demonstrate how to solve complicated problems. Changes in the new edition include:
Stronger focus on MCMC.
Revision of the computational advice in Part III.
New chapters on nonlinear models and decision analysis.
Several additional applied examples from the authors' recent research.
Additional chapters on current models for Bayesian data analysis such as nonlinear models, generalized linear mixed models, and more.
Reorganization of chapters 6 and 7 on model checking and data collection.
Bayesian computation is currently at a stage where there are many reasonable ways to compute any given posterior distribution. However, the best approach is not always clear ahead of time. Reflecting this, the new edition offers a more pluralistic presentation, giving advice on performing computations from many perspectives while making clear the importance of being aware that there are different ways to implement any given iterative simulation computation. The new approach, additional examples, and updated information make Bayesian Data Analysis an excellent introductory text and a reference that working scientists will use throughout their professional life.List of models.
List of examples.
Preface.
Fundamentals of Bayesian Inference.
Background.
Single-parameter models.
Introduction to miltiparameter models.
Large-sample inference and frequency properties of Bayesian inference.
Fundamentals of Bayesian Data Analysis.
Hierarchical models.
Model checking and improvement.
Modelling accounting for data collection.
Connection and challenges.
General advice.
Advanced Computation.
Overview of computation.
Posterior simulation.
Approximations based on posterior modes.
Special topics in computation.
Regression Models.
Introduction to regression models.
Hierarchical linear models.
Generalized linear models.
Models for robust inference.
Specific Models and Problems.
Mixture models.
Multivariate models.
Nonlinear models.
Models for missing data.
Decision analysis,
Appendixes.
Standard probability distributions.
Outline of proofs of asymptotic theorems.
Example of computation in R and Bugs.
References.
Author index.
Subject index.