Bayes and Empirical Bayes Methods for Data Analysis: (Chapman & Hall/CRC Texts in Statistical Science)

Recent advances in computing-leading to the ability to evaluate increasingly complex models-has resulted in a growing popularity of Bayes and empirical Bayes (EB) methods in statistical practice. Bayes and Empirical Bayes Methods for Data Analysis answers the need for a ready reference that can be read and appreciated by practicing statisticians as well as graduate students. It introduces Bayes and EB methods, demonstrates their usefulness in challenging applied settings, and shows how they can be implemented using modern Markov chain Monte Carlo (MCMC) computational methods. Avoiding philosophical nit-picking, it shows how properly structured Bayes and EB procedures have good frequentist and Bayesian performance both in theory and practice. The authors have chosen a very practical focus for their work, offering real solution methods to researchers with challenging problems. Beginning with an outline of the decision-theoretic tools needed to compare procedures, the book presents the basics of Bayes and EB approaches. The authors evaluate the frequentist and empirical Bayes performance of these approaches in a variety of settings and identify both virtues and drawbacks. The second half of the book stresses applications. If offers an extensive discussion of modern Bayesian computation methods-including the Gibbs sampler and the Metropolis-Hastings algorithm. It describes data analytic tasks, and offers guidelines on using a variety of special methods and models. The authors conclude with three fully worked case studies of real data sets.

Table of Contents:
Procedures and Their Properties Introduction and Motivation Structures for Inference Procedure Evaluation and other Unifying Concepts The Bayes Approach Introduction Prior Distributions Bayesian Inference Model Assessment Nonparametric Methods The Empirical Bayes Approach Introduction Nonparametric EB Point Estimation Parametric EB 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 Predictive Model Selection Special Methods and Models Ensemble Estimates Order Restricted Inference Nonlinear Models Longitudinal Data Models Continuous and Categorical Time Series Survival Analysis and Frailty Models 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 Distributional Catalog Software Guide Answers to Selected Exercises References