Bayesian Nonparametrics

by Nils Lid Hjort (Editor), Chris Holmes (Editor), Peter Müller (Editor), Stephen G. Walker (Editor)

Overview

Bayesian nonparametrics works - theoretically, computationally. The theory provides highly flexible models whose complexity grows appropriately with the amount of data. Computational issues, though challenging, are no longer intractable. All that is needed is an entry point: this intelligent book is the perfect guide to what can seem a forbidding landscape. Tutorial chapters by Ghosal, Lijoi and Prünster, Teh and Jordan, and Dunson advance from theory, to basic models and hierarchical modeling, to applications and implementation, particularly in computer science and biostatistics. These are complemented by companion chapters by the editors and Griffin and Quintana, providing additional models, examining computational issues, identifying future growth areas, and giving links to related topics. This coherent text gives ready access both to underlying principles and to state-of-the-art practice. Specific examples are drawn from information retrieval, NLP, machine vision, computational biology, biostatistics, and bioinformatics.

Product Details

ISBN-13:	9780521513463
Publisher:	Cambridge University Press
Publication date:	04/12/2010
Series:	Cambridge Series in Statistical and Probabilistic Mathematics , #28
Edition description:	New Edition
Pages:	308
Product dimensions:	7.10(w) x 10.10(h) x 0.70(d)

About the Author

Nils Lid Hjort is Professor of Mathematical Statistics in the Department of Mathematics at the University of Oslo.

Chris Holmes is Professor of Biostatistics in the Department of Statistics at the University of Oxford. He has been awarded the Guy Medal in Bronze for 2009 by the Royal Statistical Society.

Peter Müller is Professor in the Department of Biostatistics at the University of Texas M. D. Anderson Cancer Center.

Stephen G. Walker is Professor of Statistics in the Institute of Mathematics, Statistics and Actuarial Science at the University of Kent, Canterbury.

Table of Contents

List of contributors viii

An invitation to Bayesian nonparametrics Nils Lid Hjort Chris Holmes Peter Müller Stephen G. Walker 1

1 Bayesian nonparametric methods: motivation and ideas Stephen G. Walker 22

1.1 Introduction 22

1.2 Bayesian choices 24

1.3 Decision theory 26

1.4 Asymptotics 27

1.5 General posterior inference 29

1.6 Discussion 33

References 33

2 The Dirichlet process, related priors and posterior asymptotics Subhashis Ghosal 35

2.1 Introduction 35

2.2 The Dirichlet process 36

2.3 Priors related to the Dirichlet process 46

2.4 Posterior consistency 49

2.5 Convergence rates of posterior distributions 60

2.6 Adaptation and model selection 67

2.7 Bernshtein-von Mises theorems 71

2.8 Concluding remarks 74

References 76

3 Models beyond the Dirichlet process Antonio Lijoi Igor Prünster 80

3.1 Introduction 80

3.2 Models for survival analysis 86

3.3 General classes of discrete nonparametric priors 99

3.4 Models for density estimation 114

3.5 Random means 126

3.6 Concluding remarks 129

References 130

4 Further models and applications Nils Lid Hjort 137

4.1 Beta processes for survival and event history models 137

4.2 Quantile inference 144

4.3 Shape analysis 148

4.4 Time series with nonparametric correlation function 150

4.5 Concluding remarks 152

References 155

5 Hierarchical Bayesian nonparametric models with applications Yee Whye Teh Michael I. Jordan 158

5.1 Introduction 158

5.2 Hierarchical Dirichlet processes 160

5.3 Hidden Markov models with infinite state spaces 171

5.4 Hierarchical Pitman-Yor processes 177

5.5 The beta process and the Indian buffet process 184

5.6 Semiparametric models 193

5.7 Inference for hierarchical Bayesian nonparametric models 195

5.8 Discussion 202

References 203

6 Computational issues arising in Bayesian nonparametric hierarchical models Jim Griffin Chris Holmes 208

6.1 Introduction 208

6.2 Construction of finite-dimensional measures on observables 209

6.3 Recent advances in computation for Dirichlet process mixture models 211

References 221

7 Nonparametric Bayes applications to biostatistics David B. Dunson 223

7.1 Introduction 223

7.2 Hierarchical modeling with Dirichlet process priors 224

7.3 Nonparametric Bayes functional data analysis 236

7.4 Local borrowing of information and clustering 245

7.5 Borrowing information across studies and centers 248

7.6 Flexible modeling of conditional distributions 250

7.7 Bioinformatics 260

7.8 Nonparametric hypothesis testing 265

7.9 Discussion 267

References 268

8 More nonparametric Bayesian models for biostatistics Peter Müller Fernando Quintana 274

8.1 Introduction 274

8.2 Random partitions 275

8.3 Pólya trees 277

8.4 More DDP models 279

8.5 Other data formats 283

8.6 An R package for nonparametric Bayesian inference 286

8.7 Discussion 289

References 290

Author index 292

Subject index 297

Editorial Reviews

"The book looks like it will be useful to a wide range of researchers. I like that there is a lot of discussion of the models themselves as well as the computation. The book, especially in the early chapters, is more theoretical than I would prefer... But, hey, that's just my taste... on the whole I think the book is excellent. If I didn't think the book was important, I wouldn't be spending my time pointing out my disagreements with it!"
Andrew Gelman, Columbia University

"The book provides a tour de force presentation of selected topics in an emerging branch of modern statistical science, and not only justfies the reader’s curiosity, but also expands it.... The book brings together a well-structured account of a number of topics on the theory, methodology, applications, and challenges of future developments in the rapidly expanding area of Bayesian nonparametrics. Given the current dearth of books on BNP, this book will be an invaluable source of information and reference for anyone interested in BNP, be it a student, an established statistician, or a researcher in need of flexible statistical analyses."
Milovan Krnjajic, Journal of the American Statistical Association

From the Publisher