Bayesian Ideas and Data Analysis—An Introduction for Scientists and Statisticians
Andrew Viggo Metcalfe · Journal of the Royal Statistical Society Series A (Statistics in Society) · 2011
If you think that a Bayesian approach to statistical analysis is nice in principle but too complicated in practice, this book may change your mind. The authors’ enthusiasm for the subject is apparent and they have taken care that the text is generally easy to read, with some occasional wry comments that make it more amusing than a typical statistics book. The emphasis is on medical and biological cases, but a range of other applications are covered. The first quarter of the book covers the fundamental ideas of Bayesian analysis in two chapters separated by a clear introduction to Monte Carlo integration and WinBUGS14, the open source software that is used throughout the book, and preceded by a short prologue. In the prologue, the authors emphasize their conviction that data analysis should be a partnership between subject experts and statisticians, and they introduce examples from manufacturing industry, anthropology, farming and medicine. The elicitation of useful prior information is emphasized throughout the book. Chapter 3 provides practical experience by using WinBUGS for analysing binomial variables with a beta prior and discusses calculating predictive distributions, and the theoretical posterior distribution of the binomial parameter, using R. Chapter 4 has more advanced material on fundamental ideas than the general level of the book, but it can be omitted in a first reading. In contrast, Chapter 5, ‘Comparing populations’, is seen as an essential part of any course. It includes a careful discussion of inference for relative risks and odds ratios, and considers several sampling strategies. Inference for normal populations and a brief coverage of the Poisson process and sample size calculations end the chapter. Chapter 6 is an introduction to strategies for generating pseudorandom samples from probability distributions, particularly Markov chain Monte Carlo methods. I found some of the developments here quite intricate, but, again, it can be skimmed over at a first reading. Chapter 7 is a general overview of the regression topics that are covered in the later chapters, which include models for binomial and count data, and regression models for lifetime distributions as well as multiple regression. Chapter 10 deals with linear mixed models including repeated measures models, and Chapter 15, ‘Nonparametric models’, includes distribution-free regression methods and smoothing methods, and the proportional hazards model. There are three useful appendices on matrices and vectors, probability, and getting started in R, which is well chosen, and includes a note on the interface between R and WinBUGS. The exercises are an integral part of the book and are placed throughout the text, rather than at the end of chapters. They vary in difficulty; some offer practice in using WinBUGS, whereas others are more challenging and provide detail to support the development. The book does not cover time series or spatial models. There is some overlap of topics with the excellent book by Gelman et al. (2004). However, the book by Christensen and his colleagues is more of an introduction and should appeal to scientists taking courses in statistics. I think that the book is innovative for two reasons. Firstly, it provides an intermediate level course in statistics, using the Bayesian paradigm, that could be given to engineers and scientists requiring substantial statistical analysis, as well as material for a course in Bayesian statistics that is typically offered to statistics students. Secondly it shows how to perform the analyses by using WinBUGS, throughout the text. I would use this book as a basis for a course on Bayesian statistics. It is an excellent text for individual study, and students will find it a valuable reference later in their careers.