Stochastic Inequalities and Applications

workings of Markov chain Monte Carlo updating, which may be new to some readers. Explanation is complemented with relevant equations, however, proofs are omitted often. Using his introductory chapter as a springboard, Congdon then tackles model comparison and inference for numeric data (Chaps. 2 and 3) before delving into applications with categorical data. Chapter 2 is key; many examples in the following chapters refer to the metrics, such as Bayes factors or deviance information criterion (DIC), introduced here. On the other hand, although Chapter 3 provides detailed discussions on many complex regression modeling concepts (e.g., robust regression, transformations, and mixture models), it could have been omitted easily given the scope of the text. Chapter 4 provides a lower-level overview of binary and count data similar to the first chapter’s treatment of Bayesian methodology in general. Subsequent chapters expand on these ideas, and each concentrates on a specific theme. Topics include common extensions (i.e., overdispersion and zero-inflated models) in Chapter 5, random effects and latent variables (Chap. 6), and ordinal responses (Chap. 7). The book concludes with treatment of more advanced material such as temporal and spatial correlation (Chaps. 8 and 9), hierarchical and longitudinal data (Chap. 10), and missing data (Chap. 11). It is curious that the missing data chapter is the book’s last, since data augmentation is discussed extensively in earlier chapters. With Bayesian Models for Categorical Data, Congdon, once again, has written with the applied statistician in mind. The text provides adequate coverage of theoretical ideas while eschewing formal proofs or complex mathematical development. His itemized description of algorithms and model code make implementing solutions (or following along) as easy as could be expected given the nature of the subject matter. This text, unlike the author’s earlier books, contains end-of-chapter exercises which are suitable for self-study. Although the open-ended nature of the questions will promote thought, given the book’s intended audience, some might wish that solutions had been provided. Like its predecessors, Bayesian Models for Categorical Data contains numerous examples in each chapter which illustrate potential analyses on actual data. While readers, especially those new to the Bayesian inference using Gibbs sampling (BUGS) language, will appreciate the code repository (available via a dedicated ftp site), it fails to realize its full pedagogical potential. One of the compelling features of the WinBUGS software (Spiegelhalter, Thomas, Best, and Lunn 2003) is its integration of “doodles,” graphical representations of variable relationships, and standard model syntax. Not only do doodles provide additional elucidation of the model hierarchy (a picture, as they say, is worth a thousand words), model code generated from doodles is (usually) syntactically correct and is not prone to typographical errors by the user. This cannot be overstated, as Congdon’s own archive contains at least one typo in the model code (Example 4.4 which is missing a “[” between pi and its range, 1:2, in the declaration g[k] ̃dcat(pi1:2])) and therefore will not run. This is not an indictment of the author as much as an illustration of the utility of doodles, both for their illustrative capacity and preemptive model debugging. That said, the model code is an asset and the comments, while sparse, are sometimes insightful. For instance, the code accompanying Example 5.5 prevents a degenerate fitted probability: p1[i]<-max(0,min(0.999999999999,P1[i])) and the accompanying comment cites a similar problem in the BUGS mailing list. True to his earlier works, Congdon’s treatment of categorical data is ambitious, and this text contains an extensive array of examples to supplement the exposition. As such, it is perfectly suited as a reference for any practitioner. However, despite the obvious effort spent to make difficult concepts accessible to the novice, the brevity of individual discussions makes it difficult to do so. Consequently, the presentation of the material in this text is not suitable for a first course in Bayesian inference or categorical data analysis. Readers unfamiliar with the categorical data might find Agresti (2002) a more readable introduction to the topic. Nonetheless, Congdon has done a laudable job of introducing jointly the concepts of categorical data and Bayesian analysis.