Bayes and Empirical Bayes Methods for Data Analysis, Second Edition

Published:
June 22, 2000 by Chapman and Hall/CRC - 440 Pages
Author(s):
Bradley P. Carlin, University of Minnesota, Minneapolis, USA; Thomas A. Louis, Johns Hopkins Bloomberg School of Public Health, MD, USA
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ISBN 9781584881704
Cat# C1704
 

Features

  • a less technical introductory chapter comparing Bayes and frequentist inference with motivating examples
  • a gentler introduction to Gibbs sampling and full conditional distributions
  • several recent developments in MCMC, such as reversible jump MCMC, slice sampling, structured MCMC, and overrelaxation
  • an explicit description of how to estimate MCMC standard errors
  • an expanded and revised treatment of Bayesian model choice
  • new material on several spatial statistics, sequential analysis and sample size estimation for clinical trials
  • a new decision theory appendix
  • more illustrations, exercises, and solutions
  • a completely updated reference section
  • an updated guide to Bayesian software (such as WinBUGS) with worked examples
  • comprehensive 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.

    Table of Contents

    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

    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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