Monte Carlo Methods in Bayesian Computation (Springer Series in Statistics) by Ming-Hui Chen (PDF)

Description

Dealing with methods for sampling from posterior distributions and how to compute posterior quantities of interest using Markov chain Monte Carlo (MCMC) samples, this book addresses such topics as improving simulation accuracy, marginal posterior density estimation, estimation of normalizing constants, constrained parameter problems, highest posterior density interval calculations, computation of posterior modes, and posterior computations for proportional hazards models and Dirichlet process models. The authors also discuss model comparisons, including both nested and non-nested models, marginal likelihood methods, ratios of normalizing constants, Bayes factors, the Savage-Dickey density ratio, Stochastic Search Variable Selection, Bayesian Model Averaging, the reverse jump algorithm, and model adequacy using predictive and latent residual approaches. The book presents an equal mixture of theory and applications involving real data, and is intended as a graduate textbook or a reference book for a one-semester course at the advanced masters or Ph.D. level. It will also serve as a useful reference for applied or theoretical researchers as well as practitioners.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐It’s a decent book, but could use some editing. BDA is better.

⭐You need to be clear what you are looking for. If you have vaguely heard that MCMC (Monte Carlo Markov Chain) methods are a neat way to apply Bayesian ideas to practical problems, and you want to use them, then this is *not* the book for you. Go to the splendid Gilks et al, Markov Chain Monte Carlo in Practice. Also check out BUGS, which is free software, originally written by Gilks and co and improved by many others.If you want a more general introduction to Bayesian methods, then Gelman et al, Bayesian Data Analysis is excellent.If you are unclear about the controversies and want to know why the Bayesian approach is correct, and the others are flat wrong, then read Ed Jaynes book.So what is this book for. Well, I think you have to be a specialist, interested in further development of the techniques, and in the maths. As a previous reviewer has commented (correctly), in that case you probably have easy access to the journal literature and need to think carefully what extra benefits this book gives you.

⭐With advances in computing and the rediscovery of Markov Chain Monte Carlo methods and their application to Bayesian methods, there have been a number of books written on this subject in recent years. What then distinguishes this text from the others?Section 1.1 of the text “Aims” provides the objectives of the book and compares it to the other recent major works. Basically, the authors say that Tanner (1996), Gilks, Richardson and Spiegelhalter (1996), Gamerman (1997), Robert and Casella (1999) and Gelfand and Smith (2000) all offer developments in MCMC sampling. So this text only provides a brief but hopefully sufficient introduction to MCMC sampling.The main objective of the book is to develop more advanced Monte Carlo methods that speed up the computational time for specialized Bayesian problems. Problems of interest to the authors include estimating posterior means, modes and standard deviations, Bayesian equivalent of p-values, marginal posterior densities, marginal likelihoods, Bayes factors, posterior model probabilities, Bayesian credible intervals (the Bayes analogue to frequentist confidence intervals) and highest posterior probability density intervals.Chapter 1 sets the stage. It provides the objectives, an outline of the rest of the book and a list of motivating examples that will be used throughout the text.Chapter 2 then provides the brief introduction to MCMC sampling. Some theory is provided, many useful references are cited and several ideas are well illustrated through examples and figures.Chapter 3 is also introductory in nature showing how the methods of Chapter 2 can be applied to obtain various estimates based on the approximated posterior probability distribution.The rest of the book deals with specialized topics and techniques important to Bayesian inference. The book contains a wealth of theory and a good mix of applications and challenging research problems. The authors are experienced contributors to this literature.It is intended as an advanced graduate course for Ph.D. statistics student in their second or third year of graduate study. It also will serve statistical researchers with an excellent reference both for the practice and development of Bayesian inference. Applications in the area of biostatistics are emphasized but the methods apply to Bayesian statistical inference in all fields.

⭐I depend upon the Amazon reviews to help determine whether to purchase a book as most others do. When a reviewer posts four 5 star reviews of the book (out of 7 total) it biases the rating and makes one wonder whether if the reviewer has an agenda or is related to the authors. This may be a great book, but I have no confidence from the rating given here.

⭐My comment about much of this text being verbatim from papers applies mostly to another text by two of the authors (Bayesian Survival Analysis by Ibrahim, Chen, and Sinha, Springer, 2001). The degree to which the comment is true of Chen et al. (1999) is nowhere near the degree to which it is true of Ibrahim et al. (2001). But, it’s not completely false either!

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