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Bayesian Nonparametrics

Nils Lid Hjort, Chris Holmes, Peter Müller, and Stephen G. Walker, editors
Cambridge University Press
Publication Date: 
Number of Pages: 
Cambridge Series in Statistical and Probabilistic Mathematics 28
[Reviewed by
Peter Rabinovich
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Bayesian nonparametrics extends the parametric Bayesian framework to situations where the number of parameters may grow with the sample size. Thus a Bayesian nonparametric model is a Bayesian model on an infinite dimensional parameter space. “So what?” you say. The goal of this book is to answer your question.

Bayesian nonparametrics provides a range of interesting mathematical problems that alone would probably be enough to justify research — or to justify going to eat lunch. See, for example, the Chinese Restaurant Process, or the Indian Buffet Process. But where it gets really interesting (to me) is in potential applications to statistical problems that other methods cannot address.

The book is a series of well written papers by experts in the field. The book begins with detailed introductory sections placing Bayesian nonparametrics in context. Next are several papers on some of the theoretical issues of Dirichlet and related processes. The book concludes with appetizing papers on applications to machine learning and biostatistics that make me yearn for more.

The theoretical papers generally require a knowledge of graduate level theoretical statistics, say at the level of Jun Shao’s Mathematical Statistics (measure theory is used and required), whereas the applied papers require less mathematical sophistication. Also discussed are computational issues in some of the papers.

So who is this book for? Certainly a researcher who has heard the term Bayesian nonparametrics and wants to know what the subject is really about would benefit from this book. It could also be used in a seminar style graduate course, with students presenting (parts of) the various papers, being led by a professor who fills in any missing details or context. In fact, the subject is still at a stage where the theory and applications are so intertwined that such a seminar, with both theoretical and applied students, could lead to many interesting research projects.

Unfortunately, for my needs, this book is not a text. I came to this book eager to learn more, and now that my appetite has been whetted, I find that I am longing for the meal of a text, complete with exercises from which to learn the material in more depth. That being said, one of the references is to Ghosh and van der Vaart’s “Fundamentals of Nonparametric Bayesian Inference” with a publication date not too far off on the horizon, in 2010. Perhaps that book will satisfy my appetite.

Peter Rabinovitch is a Systems Architect at Research in Motion, and a PhD student in probability. When not working, he likes to eat spicy food.

An invitation to Bayesian nonparametrics Nils Lid Hjort, Chris Holmes, Peter Müller and Stephen G. Walker; 1. Bayesian nonparametric methods: motivation and ideas Stephen G. Walker; 2. The Dirichlet process, related priors, and posterior asymptotics Subhashis Ghosal; 3. Models beyond the Dirichlet process Antonio Lijoi and Igor Prünster; 4. Further models and applications Nils Lid Hjort; 5. Hierarchical Bayesian nonparametric models with applications Yee Whye Teh and Michael I. Jordan; 6. Computational issues arising in Bayesian nonparametric hierarchical models Jim Griffin and Chris Holmes; 7. Nonparametric Bayes applications to biostatistics David B. Dunson; 8. More nonparametric Bayesian models for biostatistics Peter Müller and Fernando Quintana; Author index; Subject index.