Bayesian Nonparametrics, edited by Nils Lid Hjort, Chris Holmes, Peter Müller and Stephen G. Walker, New York, Cambridge University Press, 2010, xx + 299 pp., £35.00 or US$59.00 (hardback), ISBN 978 0 521 51346 3
This book consists of a collection of articles concerning Bayesian nonparametric methods. The recent theoretical and practical aspects of Dirichlet processes are discussed. The book covers the theoretical aspects in the first four chapters, while the last four chapters document a wide range of applications from biostatistics to signal processing.
The theory of Bayesian nonparametrics presents flexible models, whose complexity increases with increasing amount of data and dimensionality. The theorems of ‘stick-breaking’ representation, Chinese restaurant process, Indian buffet process, and Bernstein–von Mises have been covered repeatedly throughout the first four chapters.
On the practical aspects, the Bayesian nonparametric techniques (such as the hierarchical Dirichlet process) have been widely applied to the areas of information retrieval, speaker diarisation, word segmentation, bioinformatics, and microarrays.
The contribution of this book is to collect most recent research of Bayesian nonparametric techniques together, with main emphasis on the use of Dirichlet process. The popularity of Dirichlet process is because that the Dirichlet prior is nonparametric and conjugate, thus presenting many opportunities to flexibly model complex data structure. The book incorporates the Bayesian philiosophy into the nonparametric concept. It also introduces Bayesian computational tools (such as the Metropolis-Hasting and Gibbs algorithms) to deal with possibly infinite number of parameters. A statistical software package in R called DRpackage has been introduced to implement Dirichlet process mixture density estimation, Pólya tree priors for density estimation, and nonparametric random effects models including generalized linear models.
The authors have fulfilled their main aim which is to introduce Bayesian nonparametrics. However, I feel this book could go even further by combining the Bayesian computational techniques with frequentist nonparametric methods. In other words, could the Bayesian techniques be well suited for solving frequentist nonparametric problems? If so, this would bring the Bayesian philosophy and frequentist philiosophy one step closer.
Overall, I enjoyed reading and reviewing this book and I feel that this book gives nice theoretical and practical viewpoints on Bayesian nonparametrics. The use of Bayesian nonparametric techniques is suitable for any statistician, who aims to analyse complex data structures with possibly infinite number of parameters. Although this book concentrates mainly on the Dirichlet process, it serves perfectly as a reference for scientists and graduate students working in the field of Bayesian data analysis.