The BUGS Book: A Practical Introduction to Bayesian Analysis

If a book has ever been so much desired in the world of statistics, it is for sure this one. Many people have been expecting it for more than 20 years, ever since the WinBUGS software has been in use. Therefore, the tens of thousands of users of WinBUGS are indebted to the leading team of the BUGS project (D. Lunn, C. Jackson, N. Best, A. Thomas, and D. Spiegelhalter) for having eventually succeeded in finalizing the writing of this book and making sure the long-held expectations are not dashed. As well explained in the preface, the BUGS project initiated at Cambridge was a very ambitious one and at the forefront of the MCMC movement that revolutionized the development of Bayesian statistics in the early 1990s after the pioneering publication of Gelfand and Smith on Gibbs sampling. This book comes out after several textbooks have already been published in the area of computational Bayesian statistics using BUGS and/or R (Gelman and Hill, 2007; Marin and Robert, 2007; Ntzoufras, 2009; Congdon, 2003, 2005, 2006, 2010; Kéry, 2010; Kéry and Schaub, 2011; and others). It is neither a theoretical book on foundations of Bayesian statistics (e.g., Bernardo and Smith, 1994; Robert, 2001) nor an academic textbook on Bayesian inference (Gelman et al, 2004; Carlin and Louis, 2008). Instead, it reflects very well the aims and spirit of the BUGS project and is meant to be a manual “for anyone who would like to apply Bayesian methods to real-world problems. ” In spite of its appearance, the book is not elementary. On the contrary, it addresses most of the critical issues faced by statisticians who want to apply Bayesian statistics in a clever and autonomous manner. Although very dense, its typical fluid British style of exposition based on real examples and simple arguments helps the reader digest without too much pain such ingredients as regression and hierarchical models, model checking and comparison, and all kinds of more sophisticated modeling approaches (spatial, mixture, time series, nonlinear with differential equations, nonparametric, etc.). The book consists of 12 chapters and three appendices specifically devoted to BUGS (A: syntax, B: functions, and C: distributions), which are very helpful for practitioners. The book is illustrated with numerous examples. The exercises are well presented and explained, and the corresponding code is made available at www.mrc-bsu.cam. ac.uk/bugs/thebugsbook. Chapter 1 (Introduction: Probability and Parameters) reminds us of the basics of probability theory. It emphasizes the originality of Bayesian statistics by considering probability (density) distribution to express uncertainty about our knowledge of parameters. Beginning with an example on mortality rates for high-risk operations, the authors point out the advantages of the Bayesian approach to answer practical questions as compared to the classical approach based on estimates, confidence intervals, and hypothesis testing. In that respect, the old dilemma of classical statistics “fixed vs. random” does not arise the same way here, as most parameters are basically fixed, but also unknown and consequently treated as random variables. I like the last two sections of this chapter devoted to the question of how to calculate quantities pertaining to probability distributions from different options (exact algebraic, exact numeric, physical experimentation, and Monte Carlo simulation), which are usually overlooked by many of us. Chapter 2 shows us how to carry out Monte Carlo simulations using BUGS for general purposes. I am not sure many people know that BUGS can be used as a pure simulator of stochastic phenomena as well as for posterior inference from data. The chapter starts with an introduction to the BUGS language, underlining the main characteristics of this graphical approach (directed acyclic graphs, DAG, with conditional independence) in contrast to a traditional sequential language. Here lies an essential aspect of BUGS explaining its generality and power, but also its importance for the user, as a grasp of the DAG structure is essential to understanding the syntax of the language (order statements in the code do not matter except for loop constraints) and to help him write his own programs efficiently. Chapter 3 sets up the framework for Bayesian inference by introducing Bayes’ theorem first in terms of events and second in terms of densities. It then illustrates it with simple but well-chosen examples on binomial and normal data with conjugate priors. The chapter ends with a comparison of Bayesian and classical approaches. A clear distinction is made between the Fisherian approach based on the concept of likelihood and p-values pertaining solely to the null hypothesis and the Neyman-Pearson philosophy derived from decision theory with error rating in the test of the null hypothesis vs. an alternative. Oddly enough for the layman, the authors show undeniably that the Bayes approach has much more in common with the approach of Fisher than with the approach of Neyman-