Bayesian Nonparametrics

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Nils Lid Hjort, Chris Holmes, Peter Müller, Stephen G. Walker
Cambridge University Press, Apr 12, 2010 - Mathematics
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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.
 

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Contents

An invitation to Bayesian nonparametrics
1
motivation and ideas
22
2 The Dirichlet process related priors and posterior asymptotics
35
3 Models beyond the Dirichlet process
80
4 Further models and applications
137
5 Hierarchical Bayesian nonparametric models with applications
158
6 Computational issues arising in Bayesian nonparametric hierarchical models
208
7 Nonparametric Bayes applications to biostatistics
223
8 More nonparametric Bayesian models for biostatistics
274
Author index
292
Subject index
297
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About the author (2010)

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.

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