My motivation for purchasing this book was to have a copy of Radford Neal's chapter (Chapter 5) on Hamiltonian Monte Carlo (HMC). For those who are new to Bayesian methods, HMC is a more recently popular way of performing Monte Carlo estimation (which is essential for modern Bayesian methods). Neal was an early proponent and exponent of HMC. So this chapter, like most in the book, comes from a leading source. HMC is important because the sophistication associated with it means that it can be much more efficient than regular MCMC. Neal makes this sophistication accessible with extensive detail, visualizations and example code listings.
It must have been an interesting task to be the person to write the first chapter in this comprehensive book. Charles Geyer does not disappoint with a review of the fundamentals that doubles as a fresh take on the fundamentals. I found this chapter re-readable in the sense that more than one reading was time well spent. Jeffrey Rosenthal writes on optimal proposal distributions in Chapter 4 with a rhetorical device I don't see in many Bayesian books. He includes Frequently Asked Questions sections in his chapter, giving the chapter a website or forum flair. Key questions are posed and answered succinctly in the FAQ sections. This is a to-the-point style great for the business/management disciplines and perfect for students in all areas.
Chapter 2 provides a brief history of 1990s-era MCMC advances. Christian Robert and George Casella summarize the excitement of the era with memorable prose. For example, they write "... an enormous number of problems that were deemed to be computational nightmares now cracked open like eggs" (p.57). Chapter 3 contains a good discussion of the benefits and challenges of reversible jump MCMC written by Yanan Fan and Scott Sisson. In Chapter 10 James Hobart discusses data augmentation and spends the last part of the chapter on parameter expanded data augmentation. Sisson and Fan also contribute Chapter 12 on likelihood-free MCMC. This chapter, like all of the previous ones, serves a second purpose as a resource for important references. The only chapter to cover marginal likelihoods/Bayes factors at any length (4 pages) is Chapter 11. This chapter is actually on importance sampling and simulated tempering, so the brief treatment makes sense. Given the large and active literature on this topic, a chapter dedicated to this would have been a bonus.
Chapters 13 through 24 discuss applications and case studies. Subject areas include biomedical applications, astrophysics, electrical impedance tomography, ornithology, rural-urban migration, and educational research. Chapter 18 focuses on spatial data and seemed to me to be more relevant for the first section of the book.
Summary: This book makes for a great reference for an intermediate/advanced practitioner of Bayesian methods. Have a look at the book on Amazon here.
Reviewed Jan 3, 2023.