A first course in Bayesian statistical methods.

*(English)*Zbl 1213.62044
Springer Texts in Statistics. New York, NY: Springer (ISBN 978-0-387-92299-7/hbk). ix, 270 p. (2009).

As mentioned in the preface, the objective of this text is to familiarize graduate students with the basic concepts of Bayesian theory and to quickly get them performing data analysis using Bayesian computational tools.

Explaining why Bayesian methods are necessary, the stage is set for introduction of Bayesian methods in the first chapter. The second chapter is on belief, probability and exchangeability, and ends with exploring the link between independence and exchangeability. Bayesian inference for one-parameter models – the binomial and the Poisson models, is the topic of Chapter 3. Monte Carlo approximations for posterior computations is dealt with in Chapter 4. Inference for normal models is discussed in Chapter 5, and posterior approximations with the Gibbs sampler and MCMC are discussed in Chapter 6. Chapter 7 discusses multivariate normal models, and models for comparison of means across groups are discussed in Chapter 8. Bayesian estimation in linear regression models, Gibbs sampling and model averaging are discussed in Chapter 9. The Metropolis-Hastings algorithm for approximating posterior distributions corresponding to any combination of prior distributions and sampling models are discussed in Chapter 10. Hierarchical models are discussed in Chapter 11, and latent variable methods for ordinal data is the title of Chapter 12. Every chapter ends with a discussion and further references. At the end, there are a good number of exercises on the topics covered in Chapters 2 to 12. Some common distributions and their properties are recorded after the exercises, followed by references. Examples and R codes are used throughout the book to illustrate the concepts and methods.

The book is written in an elementary style and graduate students will find the book comprehensive and easy to understand. The exercises help in understanding the concepts better. The book achieves its objective of familiarizing the basic concepts of Bayesian theory, and the R codes help in preparing the reader for Bayesian data analysis. There are very few misprints and the text book will be very useful to graduate students and researchers interested in learning Bayesian concepts and data analysis in a short span of time.

Explaining why Bayesian methods are necessary, the stage is set for introduction of Bayesian methods in the first chapter. The second chapter is on belief, probability and exchangeability, and ends with exploring the link between independence and exchangeability. Bayesian inference for one-parameter models – the binomial and the Poisson models, is the topic of Chapter 3. Monte Carlo approximations for posterior computations is dealt with in Chapter 4. Inference for normal models is discussed in Chapter 5, and posterior approximations with the Gibbs sampler and MCMC are discussed in Chapter 6. Chapter 7 discusses multivariate normal models, and models for comparison of means across groups are discussed in Chapter 8. Bayesian estimation in linear regression models, Gibbs sampling and model averaging are discussed in Chapter 9. The Metropolis-Hastings algorithm for approximating posterior distributions corresponding to any combination of prior distributions and sampling models are discussed in Chapter 10. Hierarchical models are discussed in Chapter 11, and latent variable methods for ordinal data is the title of Chapter 12. Every chapter ends with a discussion and further references. At the end, there are a good number of exercises on the topics covered in Chapters 2 to 12. Some common distributions and their properties are recorded after the exercises, followed by references. Examples and R codes are used throughout the book to illustrate the concepts and methods.

The book is written in an elementary style and graduate students will find the book comprehensive and easy to understand. The exercises help in understanding the concepts better. The book achieves its objective of familiarizing the basic concepts of Bayesian theory, and the R codes help in preparing the reader for Bayesian data analysis. There are very few misprints and the text book will be very useful to graduate students and researchers interested in learning Bayesian concepts and data analysis in a short span of time.

Reviewer: Ravi Sreenivasan (Mysore)

##### MSC:

62F15 | Bayesian inference |

62C10 | Bayesian problems; characterization of Bayes procedures |

62-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics |

65C05 | Monte Carlo methods |

62-07 | Data analysis (statistics) (MSC2010) |

65C60 | Computational problems in statistics (MSC2010) |