Monographs on Statistics and Applied Probability - 69: Bayes and Empirical Bayes Methods for Data Analysis

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Recent advances in computing have made it possible to evaluate complex models, leading to the increased popularity of Bayes and empirical Bayes (EB) methods in statistics. This work serves as a practical reference for both practicing statisticians and graduate students, introducing Bayes and EB methods while demonstrating their effectiveness in applied settings. It emphasizes implementation using modern Markov chain Monte Carlo (MCMC) techniques, showcasing how well-structured Bayes and EB procedures perform in both frequentist and Bayesian contexts without delving into philosophical debates. The authors adopt a practical approach, providing real solution methods for researchers facing challenging problems. They begin by outlining the decision-theoretic tools necessary for comparing procedures, followed by an introduction to the fundamentals of Bayes and EB approaches. The performance of these methods is evaluated across various scenarios, highlighting their strengths and weaknesses. The latter half of the work focuses on applications, offering an in-depth discussion of contemporary Bayesian computation methods, including the Gibbs sampler and the Metropolis-Hastings algorithm. It also covers data analytic tasks and provides guidelines for utilizing various specialized methods and models. The book concludes with three comprehensive case studies based on real datasets, illustrating the application of the discussed methods.