Bayesian Data Analysis

The authors suggest three audiences: a graduate text and a first-principles general introduction to Bayesian inference as well as a handbook of Bayesian methods in applied statistics for general users. The book certainly fits the first very well, although it would require that the instructor supplement end-of-chapter problems (and in-text exercises) with further details. As either a general introduction or a text for a general user it should be noted that the book requires familiarity with probability and statistical modelling. It does not have the detailed development of theory in a way that is presented by a text such as Robert (2001); nor does it have the detailed development of algorithms such as Robert and Casella (1999). What it does do though is motivates Bayesian methods through applications. At the same time, it is definitely not an applied statistics cookbook. However brief or informal the mathematical development may seem to some readers, the theoretical underpinnings of models and fitting methods are lucidly outlined and are readily followed. Indeed, there are chapters such as Chapter 8 ‘Modeling accounting for data collection’ which outlines key topics such as survey methods, randomized trials, causal inference, censoring and truncation and Chapter 18 ‘Models for missing data’. It seems fairly rare to find these topics in many non-specialist books. The third edition sees an addition of two new authors and new material in terms of the models fitted such as Chapter 20 (‘Basis function models’), Chapter 21 (‘Gaussian process models’) and Chapter 23 (‘Dirichlet process models’) as well as the fitting methods. For the material presented on fitting algorithms, perhaps Hamiltonian Monte Carlo sampling (section 12.4) and STAN software have pride of place; nevertheless this is not a software handbook and most material can be read independently of thoughts about particular software implementation. Indeed, mention is also given to variational inference, expectation propagation, approximate Bayesian computation and a very brief mention of particle filtering (page 300; not indexed that I could see) as well as material on posterior approximations. Appendix C, as in earlier editions, provides a very brief overview of computer implementation for Gibbs, Metropolis and Hamiltonian Monte Carlo sampling by using both R coding to see the workings as well as STAN as an introduction to this software. Where this book excels is that it contains a wealth of practical experience, set in the context of a coherently presented text on modern Bayesian modelling. Prior choice is explored in many applications such as section 5.7 which examines priors for hierarchical variance parameters. Chapter 6 covers ‘Model checking’ and Chapter 7 ‘Evaluating, comparing and expanding models’. I guess that these chapters set out the authors’ opinions (for example out-of-sample predictions are rated highly) and that other authors might view things differently (placing more emphasis on regularization methods) but they deserve careful attention by drawing attention to these often neglected topics. Overall, this is an excellent book. It would be a valuable addition to any institutional library. The third edition offers much that is not contained in the second and it is worth upgrading. In terms of personal purchase the decision rests entirely on what the reader is looking for in a Bayesian textbook. This book is quite clear in what it wishes to be, and it fulfils that aim admirably.