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BAYES AND EMPIRICAL BAYES METHODS FOR DATA ANALYSIS

Bayesian

data

analysi

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由Bradley P. Carlin等人编著的Bayesian statistical learning方面的经典教材，覆盖了贝叶斯统计推断的系统理论，包括Bayesian inference method, empirical Bayes approaches, Bayesian computation algorithms, Model selection 以及 advanced Bayesian models 等章节.

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BAYES AND

EMPIRICAL

BAYES

METHODS

FOR

DATA ANALYSIS

Second edition

Bradley P. Carlin

Professor, Division of Biostatistics,

School of Public Health, University of Minnesota,

Minneapolis,

and

Thomas A. Louis

Senior Statistician,

The RAND Corporation,

Santa Monica, CA

CHAPMAN & HALL/CRC

A CRC Press Company

Boca Raton London New York Washington, D.C.

Library of Congress Cataloging-in-Publication Data

Carlin, Bradley P.

Bayes and empirical bayes methods for data analysis / Bradley P. Carlin and Thomas A.

Louis--2nd ed.



cm. (Texts in statistical science series)

Previous ed.: New York: Chapman & Hall, 1996.

Includes bibliographical references and indexes.

ISBN 58488-170-4

Bayesian statistical decision theory. I. Louis, Thomas A., II. Title. III. Texts

in statistical science

QA279.5.C36 2000

519'.5842-dc21



00-038242

CIP

This book contains information obtained from authentic and highly regarded sources. Reprinted material

is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable

efforts have been made to publish reliable data and information, but the author and the publisher cannot

assume responsibility for the validity of all materials or for the consequences of their use.

Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic

or mechanical, including photocopying, microfilming, and recording, or by any information storage or

retrieval system, without prior permission in writing from the publisher.

The consent of CRC Press LLC does not extend to copying for general distribution, for promotion, for

creating new works, or for resale. Specific permission must be obtained in writing from CRC Press LLC

for such copying.

Direct all inquiries to CRC Press LLC, 2000 N.W. Corporate Blvd., Boca Raton, Florida 33431.

Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are

used only for identification and explanation, without intent to infringe.

Visit the CRC Press Web site at

www.crcpress.co

No claim to original U.S. Government works

International Standard Book Number 1-58488-170-4

Library of Congress Card Number 00-38242

Printed in the United States of America



3 4 5 6 7 8 9 0

Printed on acid-free paper

Contents

Preface to the Second Edition

Preface to the First Edition



Approaches for statistical inference

1.1

Introduction

1.2



Motivating vignettes

1.2.1



Personal probability

1.2.2

Missing data

1.2.3

Bioassay

1.2.4

Attenuation adjustment

1.3



Defining the approaches

1.4



The Bayes-frequentist controversy

1.5



Some basic Bayesian models

1.5.1



A Gaussian/Gaussian (normal/normal) model

1.5.2



A beta/binomial model

1.6

Exercises

The Bayes approach

2.1

Introduction

2.2



Prior distributions

2.2.1



Elicited priors

2.2.2



Conjugate priors

2.2.3



Noninformative priors

2.2.4

Other prior construction methods

2.3



Bayesian inference

2.3.1



Point estimation

2.3.2

Interval estimation

2.3.3



Hypothesis testing and Bayes factors

2.3.4

Example: Consumer preference data

2.4

Model assessment

2.4.1



Diagnostic measures

2.4.2

Model averaging

2.5

Nonparametric methods

2.6

Exercises

The empirical Bayes approach

3.1

Introduction

3.2



Nonparametric EB (NPEB) point estimation

3.2.1



Compound sampling models

3.2.2

Simple NPEB (Robbins' method)

3.2.3

Example: Accident data

3.3



Parametric EB (PEB) point estimation

3.3.1



Gaussian/Gaussian models

3.3.2



Beta/binomial model

3.3.3



EB performance of the PEB

3.3.4

Stein estimation

3.4



Computation via the EM algorithm

3.4.1



EM for PEB

3.4.2



Computing the observed information

3.4.3

EM for NPEB

3.4.4

Speeding convergence and generalizations

3.5



Interval estimation

3.5.1

Morris' approach

3.5.2



Marginal posterior approach

3.5.3

Bias correction approach

3.6



Generalization to regression structures

3.7

Exercises

Performance of Bayes procedures

4.1



Bayesian processing

4.1.1



Univariate stretching with a two-point prior

4.1.2



Multivariate Gaussian model

4.2



Frequentist performance: Point estimates

4.2.1



Gaussian/Gaussian model

4.2.2



Beta/binomial model

4.2.3

Generalization

4.3

Frequentist performance: Confidence intervals

4.3.1



Beta/binomial model

4.3.2

Fieller-Creasy problem

4.4



Empirical Bayes performance

4.4.1

Point estimation

4.4.2

Interval estimation

4.5



Design of experiments

4.5.1



Bayesian design for frequentist analysis

4.5.2



Bayesian design for Bayesian analysis

4.6

Exercises

Bayesian computation

5.1

Introduction

5.2



Asymptotic methods

5.2.1



Normal approximation

5.2.2



Laplace's method

5.3



Noniterative Monte Carlo methods

5.3.1

Direct sampling

5.3.2

Indirect

methods

5.4



Markov chain Monte Carlo methods

5.4.1



Substitution sampling and data augmentation

5.4.2



Gibbs sampling

5.4.3

Metropolis-Hastings algorithm

5.4.4



Hybrid forms and other algorithms

5.4.5

Variance estimation

5.4.6



Convergence monitoring and diagnosis

5.5

Exercises



Model criticism and selection

6.1



Bayesian robustness

6.1.1

Sensitivity analysis

6.1.2

Prior partitioning

6.2



Model assessment

6.3



Hayes factors via marginal density estimation

6.3.1

Direct methods

6.3.2



Using Gibbs sampler output

6.3.3



Using Metropolis-Hastings output

6.4



Bayes factors via sampling over the model space

6.4.1



Product space search

6.4.2



"Metropolized" product space search

6.4.3



Reversible jump MCMC

6.4.4



Using partial analytic structure

6.5



Other model selection methods

6.5.1



Penalized likelihood criteria

6.5.2



Predictive model selection

6.6

Exercises

Special methods and models

7.1



Estimating histograms and ranks

7.1.1



Model and inferential goals

7.1.2



Triple goal estimates

7.1.3



Smoothing and robustness

7.2



Order restricted inference

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