Gelman A. et al. Bayesian Data Analysis

Chapman and Hall/CRC – 2003, 696 pages, 2nd edition
ISBN: 158488388X, 9781584883883Incorporating 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 MCMCRevision of the computational advice in Part IIINew chapters on nonlinear models and decision analysisSeveral additional applied examples from the authors' recent researchAdditional chapters on current models for Bayesian data analysis such as nonlinear models, generalized linear mixed models, and moreReorganization of chapters 6 and 7 on model checking and data collectionBayesian 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.Fundamentals of Bayesian Inference
Background
Single-Parameter Models
Introduction to Multiparameter Models
Large-Sample Inference and Connections to Standard Statistical Methods
Fundamentals of Bayesian Data Analysis
Hierarchical Models
Model Checking and Improvement
Modeling Accounting for Data Collection
Connections and Controversies
General Advice
Advanced Computation
Overview of Computation
Posterior Simulation
Approximations Based on Posterior Modes
Topics in Computation
Regression Models
Introduction to Regression Models
Hierarchical Linear Models
Generalized Linear Models
Models for Robust Inference and Sensitivity Analysis
Analysis of Variance
Specific Models and Problems
Mixture Models
Multivariate Models
Nonlinear Models
Models for Missing Data
Decision Analysis
Appendices
A: Standard Probability Distributions
B: Outline of Proofs of Asymptotic Theorems
C: Example of Computation in R and Bugs