Bayesian Nonparametrics

1. Front Matter

   Pages i-xii

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2. Introduction: Why Bayesian Nonparametrics—An Overview and Summary

   Pages 1-8

3. Preliminaries and the Finite Dimensional Case

   Pages 9-55

4. M(χ) and Priors on M(χ)

   Pages 57-86

5. Dirichlet and Polya tree process

   Pages 87-120

6. Consistency Theorems

   Pages 121-139

7. Density Estimation

   Pages 141-180

8. Inference for Location Parameter

   Pages 181-195

9. Regression Problems

   Pages 197-220

10. Uniform Distribution on Infinite-Dimensional Spaces

    Pages 221-235

11. Survival Analysis—Dirichlet Priors

    Pages 237-252

12. Neutral to the Right Priors

    Pages 253-280

13. Exercises

    Pages 281-284

14. Back Matter

    Pages 285-305

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Bayesian nonparametrics has grown tremendously in the last three decades, especially in the last few years. This book is the first systematic treatment of Bayesian nonparametric methods and the theory behind them. While the book is of special interest to Bayesians, it will also appeal to statisticians in general because Bayesian nonparametrics offers a whole continuous spectrum of robust alternatives to purely parametric and purely nonparametric methods of classical statistics. The book is primarily aimed at graduate students and can be used as the text for a graduate course in Bayesian nonparametrics. Though the emphasis of the book is on nonparametrics, there is a substantial chapter on asymptotics of classical Bayesian parametric models. Jayanta Ghosh has been Director and Jawaharlal Nehru Professor at the Indian Statistical Institute and President of the International Statistical Institute. He is currently professor of statistics at Purdue University. He has been editor of Sankhya and served on the editorial boards of several journals including the Annals of Statistics. Apart from Bayesian analysis, his interests include asymptotics, stochastic modeling, high dimensional model selection, reliability and survival analysis and bioinformatics. R.V. Ramamoorthi is professor at the Department of Statistics and Probability at Michigan State University. He has published papers in the areas of sufficiency invariance, comparison of experiments, nonparametric survival analysis and Bayesian analysis. In addition to Bayesian nonparametrics, he is currently interested in Bayesian networks and graphical models. He is on the editorial board of Sankhya.

• Survival analysis
• Variance
• probability
• statistics

From the reviews:

"The book will find a place as essential study for researchers in this modern area of statistics. It is well written, the signposts are clearly displayed throughout, and the literature appears to be well documented." ISI Short Book Reviews, Vol. 24/1, Apr. 2004

"This is the first book to present an exhaustive and comprehensive treatment of Bayesian nonparametrics. Ghosh and Ramamoorthi present the theoretical underpinnings of nonparametric priors in a rigorous yet extremely lucid style...It is indispensable to any serious Bayesian. It is bound to become a classic in Bayesian nonparametrics." Sankhya, 2004, Vol. 66, Part 1

"This new monograph by Ghosh and Ramamoorthi fulfills the need for an advanced and complete textbook at the graduate level, dealing with the theoretical aspects of Bayesian nonparametrics and Bayesian asymptotics. This is a noteworthy book that covers, with mathematical rigor, a broad class of subjects...Bayesian Nonparametrics will give researchers in the area of nonparametric and semiparametric Bayesian inference a well-written introduction to the theoretical aspects of the discipline, and it should be considered a must for anyone interested in Bayesian asymptotics." Journal of the American Statistical Association, September 2004

"This is the first book to present an exhaustive and comprehensive treatment of Bayesian nonparametrics. Ghosh and Ramamoorthi present the theoretical underpinnings of nonparametric priors in a rigourous yet extremely lucid style. … It is an excellent book for a serious reader … . This book is unique in doing all this in an elegant way – the proofs are all presented in an eminently readable style. It is indispensable to any serious Bayesian. It is bound to become a classic in Bayesian nonparametrics." (Jayaram Sethuraman, Sankhya: The Indian Journal of Statistics, Vol. 66 (1), 2004)

"The style of the book is wellsummarized in the following quotations: ‘This monograph provides a systematic, theoretical development of the subject’. … The book will find a place as essential study for researches in this modern area of statistics. It is well written, the signposts are clearly displayed throughout, and the literature appears to be well documented." (M. J. Crowder, Short Book Reviews, Vol. 24 (1), 2004)

"The present monograph gives a nice overview on the state of the art in Bayesian nonparametrics. … The reader will find a huge amount of references. In conclusion, the present book can be recommended for research and advanced lectures and seminars." (Arnold Janssen, Zentralblatt MATH, Vol. 1029, 2004)

"Nonparametrics and other infinite-dimensional problems have been difficult for Bayesians to deal with for various reasons. … In view of all these formidable difficulties, the advances achieved in this field in recent years are truly remarkable. The book by Ghosh and Ramamoorthi discusses theoretical aspects of these advances in Bayesian nonparametrics and Bayesian asymptotics. … The book is suggested as an introductory text at the graduate level. … It can also serve as an excellent reference book for researchers." (Mohan Delampady, Mathematical Reviews, 2004g)

• Statistics-Mathematics Division, Indian Statistical Institute, Kolkata, India

  J. K. Ghosh

• Statistics and Probability, Michigan State University, East Lansing, USA

  R. V. Ramamoorthi

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