Bayesian Nonparametrics : Cambridge Series in Statistical and Probabilistic Mathematics - Nils Lid Hjort

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Bayesian Nonparametrics

By: Nils Lid Hjort (Editor), Chris Holmes (Editor), Peter MÃ¼ller (Editor), Stephen G. Walker (Editor)

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Hardcover | 24 June 2010

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Hardcover
308 Pages

Dimensions(cm)
25.4 x 17.78 x 1.91

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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 Pruenster, 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.

Industry 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

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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
Table of Contents provided by Ingram. All Rights Reserved.

Bayesian Nonparametrics

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

More in Probability & Statistics

The Maths Book

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The Art of Uncertainty

How to Navigate Chance, Ignorance, Risk and Luck

Fooled By Randomness

The Hidden Role of Chance in Life and in the Markets

Understanding Structural Equation Models

Models of Relationships Between Variables

Understanding Structural Equation Models

Models of Relationships Between Variables

The Art of Statistics

Learning from Data

Speed

How it Explains the World

Sampling Theory and Practice

Probability and Statistics for Science and Engineering

Practical Statistics

New Perspectives in Statistical Modeling

Mathematical and Statistical Methods for Actuarial Sciences

Mathematical and Statistical Methods for Actuarial Sciences

Applied Multivariate Statistical Analysis

Foundations of Statistics

Data Assimilation

Methods, Modeling and Applications

Everything Is Predictable

How Bayes' Remarkable Theorem Explains the World

Psychology Statistics For Dummies

For Dummies

Introduction to Medical Statistics

4th edition

On the Edge

The Art of Risking Everything

Hands-On Programming with R

Write Your Own Functions and Simulations

Statistics without Tears

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Statistical Rethinking

2nd Edition - A Bayesian Course with Examples in R and STAN

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