Bayes and Empirical Bayes Methods for Data Analysis

About this book

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.

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

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