Bayesian Nonparametrics

Bayesian Nonparametrics

by Nils Lid Hjort
     
 

ISBN-10: 0521513464

ISBN-13: 9780521513463

Pub. Date: 04/30/2010

Publisher: Cambridge University Press

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.

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:
04/30/2010
Series:
Cambridge Series in Statistical and Probabilistic Mathematics Series, #28
Edition description:
New Edition
Pages:
308
Product dimensions:
7.10(w) x 10.10(h) x 0.70(d)

Related Subjects

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

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