The second edition of D. S. Sivia’s Data Analysis: A Bayesian Tutorial offers readers an alternative approach to the frequentist methods of statistical inference that are typically covered in a data analysis course. The book avoids what the author describes as a “cook-book recipe mentality” by using examples to demonstrate the use of various Bayesian methods and models, rather than providing a long list of methods with only few examples illustrating the applicability of a method. This tutorial should be accessible to individuals with a familiarity in multivariable calculus and linear algebra and many of the examples may be of interest to scientists who have this mathematical background. Part 1 of the book motivates the use of Bayesian methods and covers basic probability, parameter estimation, model selection, and choice of prior probabilities. Part 2 covers advanced topics such as non-parametric estimation, experimental design, and least-square procedures. J. Skilling contributed two new chapters to the second edition which describe nested sampling, a new numerical technique for doing Bayesian computations.
One of the strengths of this book is the author’s ability to motivate the use of Bayesian methods through simple yet effective examples. As the text progresses the examples become more complicated and cover issues like image processing and crystallography. The first chapter also provides a short history of probability and the differences between the Bayesian and frequentist perspectives on statistical inference. One of the weaknesses of the book is that many of the section descriptions are rather vague which may limit the reader’s ability to quickly find a specific topic of interest. The new chapters provided by J. Skilling do offer C programs that can fit some of the Bayesian models discussed in the book, but I didn’t find any references to other software programs that can be used to fit these models. In the end though, I think this book will provide the reader a nice mix of Bayesian philosophy and applications.