“This original, thought-provoking, and transforming, book is much much more than an implementation manual for Bayesian Data Analysis, even though it shares almost the same perspective. (The first sentence of the book states that the authors’ `conceptions of statistical practice, and of Bayesian statistics, have changed over the years’.) By providing a modus vivendi for undertaking Bayesian modelling from scratch in realistic settings where models are not magicked out of the blue, the authors explicit and rationalise the many steps required by such a bottom-up modelling protocol (`not a checklist, not a cookbook’, and not a flowchart!) in real situations. The contents read very well and very smoothly, with a seamless conjunction of intuition, modelling advices, computational details, and comparison tools. While unsurprisingly Bayesian, the perspective adopted therein remains both open and inclusive, with a welcome humility about the limitations and challenges of Bayesian workflows. This book should thus appeal to and profit a wide variety of readers, as providing guidance through an extensive collection of highly detailed examples, with shared code and exercises.”
This book proposes a modus vivendi for Bayesian modelling in applied, realistic Bayesian analysis, where models are not magicked out of the blue. It thus emphases iterative model building, model checking, computational troubleshooting, and simulated-data experimentation, filling a gap that looks glaring in retrospect. It particularly targets users and developers of Stan, with code excerpts in R and Stan. It consists of four parts:
- background on Bayesian methods and computational tools;
- the Bayesian workflow proper, namely building a statistical model from its components, together with its assessment tools;
- the computational aspects of fitting models, diagnosing convergence and assessing calibration;
- case studies.
I was eagerly waiting for the book, as I knew Andrew, Aki, and Richard had been working on it for a few years. (The quote above is the blurb I wrote upon request from the publisher.)
The tenets of BaWoFlo—if I may resort to this acronym!—are (i) fitting multiple models, (ii) applying methods repeatedly, and (iii) resorting to simulated-data experiments, which should not come as a surprise to readers of BDA. As noted in the introduction, the protocol exposed therein can also benefit non-Bayesian experimenters. This agrees with the highly moderate, “M-open”, agnostic approach to Bayesianism adopted by the authors (“there is no safe haven”). I also welcome and share their humble perspective about the limitations and challenges of Bayesian workflows.
Examples are treated in full detail, with successive modelling and computational choices profusely commented, which is a big plus for such a practical book. This starts as early as Chapter 4, with a multiple-choice exam example. Indeed, there cannot be general principles or a generic theory that would make the approach foolproof. See, e.g., “A data model is not just a ‘likelihood’” (p.70), as when the data model is not fully generative. I very much liked the section on choosing priors (5.6), and the very rich graphs (see, e.g., Chapter 8) for assessing the impact of prior and likelihood, as well as for predictive checks. In coherent continuation of the authors’ earlier work, the book advocates LOO methods and model stacking rather than model averaging. (With a surprisingly anti-Ockham perspective in Section 9.7.)
The MCMC coverage is unsurprising, with \(\hat R\) at the forefront. Chapter 12, on using fast experiments to detect fitting or computational issues, is very nice. The book builds on the immense corpus of work achieved by the authors over the decades (for the most senior ones!). By contrast, the chapter on approximate solutions (13) is way too short, and the same goes for those on calibration and software development.
The book is very US-centric, unsurprisingly given Andrew’s focus on political science. Some sections are reminiscent of Andrew’s blog entries (or the opposite). The (football) World Cup example was initiated when Andrew was in France, during the 2014 World Cup, and as a result (?) the names of the teams are in French! One chapter also reanalyses the birthdate data displayed on the cover of BDA.
Mileage varies on the applied chapters, depending on the example. A dog chapter is followed by a cat chapter! Not that the (stat)dog experiment was in any way enjoyable, especially for the dogs. Maybe the cats were running it! And then come chapters on roaches and sharks. There is also a frightening flowchart (Fig. 2.1)! And the book ends with an appendix on going through BDA to better understand BaWoFlo
[The usual disclaimer applies, namely that this review is likely to appear later in CHANCE, in my book reviews column.]
Bayes Rules!
Nature 
