Bayesian Nonparametrics

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 Pruuml;nster, 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.

Nils Lid Hjort is Professor of Mathematical Statistics in the Department of Mathematics at the University of Oslo, Norway. Chris Holmes is Professor of Biostatistics in the Department of Statistics at the University of Oxford, Programme Leader in Statistical Genomics at MRC Harwell and member of the Oxford-Man Institute. Peter Mller 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.

List of contributors	p. viii
An invitation to Bayesian nonparametrics	p. 1
Bayesian nonparametric methods: motivation and ideas	p. 22
Introduction	p. 22
Bayesian choices	p. 24
Decision theory	p. 26
Asymptotics	p. 27
General posterior inference	p. 29
Discussion	p. 33
References	p. 33
The Dirichlet process, related priors and posterior asymptotics	p. 35
Introduction	p. 35
The Dirichlet process	p. 36
Priors related to the Dirichlet process	p. 46
Posterior consistency	p. 49
Convergence rates of posterior distributions	p. 60
Adaptation and model selection	p. 67
Bernshtein-von Mises theorems	p. 71
Concluding remarks	p. 74
References	p. 76
Models beyond the Dirichlet process	p. 80
Introduction	p. 80
Models for survival analysis	p. 86
General classes of discrete nonparametric priors	p. 99
Models for density estimation	p. 114
Random means	p. 126
Concluding remarks	p. 129
References	p. 130
Further models and applications	p. 137
Beta processes for survival and event history models	p. 137
Quantile inference	p. 144
Shape analysis	p. 148
Time series with nonparametric correlation function	p. 150
Concluding remarks	p. 152
References	p. 155
Hierarchical Bayesian nonparametric models with applications	p. 158
Introduction	p. 158
Hierarchical Dirichlet processes	p. 160
Hidden Markov models with infinite state spaces	p. 171
Hierarchical Pitman-Yor processes	p. 177
The beta process and the Indian buffet process	p. 184
Semiparametric models	p. 193
Inference for hierarchical Bayesian nonparametric models	p. 195
Discussion	p. 202
References	p. 203
Computational issues arising in Bayesian nonparametric hierarchical models	p. 208
Introduction	p. 208
Construction of finite-dimensional measures on observables	p. 209
Recent advances in computation for Dirichlet process mixture models	p. 211
References	p. 221
Nonparametric Bayes applications to biostatistics	p. 223
Introduction	p. 223
Hierarchical modeling with Dirichlet process priors	p. 224
Nonparametric Bayes functional data analysis	p. 236
Local borrowing of information and clustering	p. 245
Borrowing information across studies and centers	p. 248
Flexible modeling of conditional distributions	p. 250
Bioinformatics	p. 260
Nonparametric hypothesis testing	p. 265
Discussion	p. 267
References	p. 268
More nonparametric Bayesian models for biostatistics	p. 274
Introduction	p. 274
Random partitions	p. 275
Pólya trees	p. 277
More DDP models	p. 279
Other data formats	p. 283
An R package for nonparametric Bayesian inference	p. 286
Discussion	p. 289
References	p. 290
Author index	p. 292
Subject index	p. 297
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Bayesian Nonparametrics

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