Features a less technical introductory chapter comparing Bayes and frequentist inference with motivating examplesa gentler introduction to Gibbs sampling and full conditional distributions several recent developments in MCMC, such as reversible jump MCMC, slice sampling, structured MCMC, and overrelaxationan explicit description of how to estimate MCMC standard errors an expanded and revised treatment of Bayesian model choicenew material on several spatial statistics, sequential analysis and sample size estimation for clinical trials a new decision theory appendixmore illustrations, exercises, and solutionsa completely updated reference sectionan updated guide to Bayesian software (such as WinBUGS) with worked examplescomprehensive subject and author indices.
Summary In recent years, Bayes and empirical Bayes (EB) methods have continued to increase in popularity and impact. Building on the first edition of their popular text, Carlin and Louis introduce these methods, demonstrate their usefulness in challenging applied settings, and show how they can be implemented using modern Markov chain Monte Carlo (MCMC) methods. Their presentation is accessible to those new to Bayes and empirical Bayes methods, while providing in-depth coverage valuable to seasoned practitioners. With its broad appeal as a text for those in biomedical science, education, social science, agriculture, and engineering, this second edition offers a relatively gentle and comprehensive introduction for students and practitioners already familiar with more traditional frequentist statistical methods. Focusing on practical tools for data analysis, the book shows how properly structured Bayes and EB procedures typically have good frequentist and Bayesian performance, both in theory and in practice.
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APPROACHES FOR STATISTICAL INFERENCE
Introduction
Motivating Vignettes
Defining the approaches
The Bayes-Frequentist Controversy
Some Basic Bayesian Models
THE BAYES APPROACH
Introduction
Prior Distributions
Bayesian Inference
Model Assessment
THE EMPIRICAL BAYES APPROACH
Introduction
Nonparametric EB (NPEB) Point Estimation
Parametric EB (PEB) Point Estimation
Computation via the EM Algorithm
Interval Estimation
Generalization to Regression Structures
PERFORMANCE OF BAYES PROCEDURES
Bayesian Processing
Frequentist Performance: Point Estimates
Frequentist Performance: Confidence Intervals
Empirical Bayes Performance
Design of Experiments
BAYESIAN COMPUTATION
Introduction
Asymptotic Methods
Noniterative Monte Carlo Methods
Markov Chain Monte Carlo Methods
MODEL CRITICISM AND SELECTION
Bayesian Robustness
Model Assessment
Bayes Factors via Marginal Density Estimation
Bayes Factors via Sampling over the Model Space
Other Model Selection Methods
SPECIAL METHODS AND MODELS
Estimating Histograms and Ranks
Order Restricted Inference
Nonlinear Models
Longitudinal Data Models
Continuous and Categorical Time Series
Survival Analysis and Frailty Models
Sequential Analysis
Spatial and Spatio-Temporal Models
CASE STUDIES
Analysis of Longitudinal AIDS Data
Robust Analysis of Clinical Trials
Spatio-Temporal Mapping of Lung Cancer Rates
APPENDICES
A Distributional Catalog
Decision Theory
Software Guide
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Editorial Reviews
About the Second Edition:
"The writing is excellent and the worked examples are also excellent for understanding the methods. In summary, I recommend Bayes and Empirical Bayes Methods for Data Analysis for advanced graduate students and all research workers."
-Olaf Berke in Computational Statistics & Data Analysis, January 2001
"...particularly commends the book to practising biometricians who want to explore the potential for using Bayesian methods in their own work."
-Biometrics, Vol. 57, No. 3, September 2001
"...the book is beautifully written and many of the questions it raises - and most of the answers provided - are of concern for the applied statistician whether Bayesian, frequentist or likelihoodist."
-Guadalupe Gomez, Statistics in Medicine Vol 21, #23 Dec 15 2002.
About the First Edition:
"...an important and timely addition to applied statistics…the writing is excellent, and the authors are able to present an amazing amount of material cogently in [a] smaller book…the reader reaps the benefits of being in the hands of a true master…"
-Journal of American Statistical Association
"…an excellent exposition of Bayes and empirical Bayes methods…gives a well-balanced mathematical and computational treatment of Bayes and empirical Bayes paradigms, and nicely examines the similarities and contrasts in the two approaches."
-Short Book Reviews of the ISI
"…and impressive compendium of the mathematical techniques underlying Bayes and empirical Bayes methods…"
-American Journal of Epidemiology
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