Robust Bayesian Analysis

430 Pages·2000·12.94 MB·English

by  James O. Berger, David Ríos Insua, Fabrizio Ruggeri (auth.), David Ríos Insua, Fabrizio Ruggeri (eds.)

Lecture Notes in Statistics
Edited by P. Bickel, P. Diggle, S. Fienberg, K. Krickeberg,
I. Olkin, N. Wermuth, S. Zeger
Springer Science+Business Media, LLC
David Rios Insua
Fabrizio Ruggeri (Editors)
Robust Bayesian Analysis
David Rios Insua Fabrizio Ruggeri
ESCET-URJC CNR IAMI
Tulipan s/n Via Ampere 56
28933 Mostoles, Madrid [-20131 Milano
Spain Italy
Library of Congress Cataloging-in-Publication Data
Robust Bayesian analysis / editors, David Rios Insua, Fabrizio Ruggeri.
p. cm. — (Lecture notes in statistics ; 152)
Includes bibliographical references.
ISBN 978-0-387-98866-5 ISBN 978-1-4612-1306-2 (eBook)
DOI 10.1007/978-1-4612-1306-2
1. Bayesian statistical decision theory. I. Rios Insua, David, 1964- II. Ruggeri,
Fabrizio. III. Lecture notes in statistics (Springer-Verlag); v. 152.
QA279.5 .R64 2000
519.5'42--dc21
00-041912
Printed on acid-free paper.
© 2000 Springer Science+Business Media New York
Originally published by Springer-Verlag New York in 2000
All rights reserved. This work may not b e translated or copied in whole or in part without the written
permission of the publisher (Springer Science+Business Media, LLC) ,
except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with
any form of information storage and retrieval, electronic adaptation, computer software, or by similar or
dissimilar methodology now known or hereafter developed is forbidden.
The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the former
are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks
and Merchandise Marks Act, may accordingly be used freely b y anyone.
Camera ready copy provided by the editors.
9 8 7 6 5 4 3 21
ISBN 978-0-387-98866-5 SPIN 10728773
Preface
Robust Bayesian analysis aims at overcoming the traditional objection to
Bayesian analysis of its dependence on subjective inputs, mainly the prior
and the loss. Its purpose is the determination of the impact of the inputs
to a Bayesian analysis (the prior, the loss and the model) on its output
when the inputs range in certain classes. If the impact is considerable,
there is sensitivity and we should attempt to further refine the information
available, perhaps through additional constraints on the incumbent classes
and/ or obtaining additional data; if the impact is not important, robustness
holds and no further analysis and refinement would be required. Robust
Bayesian analysis has been widely accepted by Bayesian statisticians; for
a while it was even a main research topic in the field. However, to a great
extent, their impact is yet to be seen in applied settings.
This volume, therefore, presents an overview of the current state of robust
Bayesian methods and their applications and identifies topics of further in
terest in the area. The papers in the volume are divided into nine parts
covering the main aspects of the field. The first one provides an overview
of Bayesian robustness at a non-technical level. The paper in Part II con
cerns foundational aspects and describes decision-theoretical axiomatisa
tions leading to the robust Bayesian paradigm, motivating reasons for which
robust analysis is practically unavoidable within Bayesian analysis. Chap
ters in Part III discuss sensitivity to the prior, illustrating the key results
in global and local robustness, along with their uses and limitations. Likeli
hood robustness is the topic of the paper in Part IV, whereas the papers in
Part V address the issue of loss robustness, focussing on ranges of posterior
expected losses, efficient sets and stability of Bayes decisions. The robust
Bayesian approach is compared with other statistical methods in Part VI,
specifically discussing sensitivity issues in Bayesian model selection and
Bayesian nonparametrics and illustrating the r -minimax paradigm. Rel
evant algorithms in robust Bayesian analysis are presented in the papers
in Part VII. Part VIII presents a discussion of case studies using a robust
Bayesian approach, from medical decision making and statistics, economics
and reliability. Finally, an extensive bibliography on Bayesian robustness
concludes the volume.
We are grateful to all the contributors for their efforts in preparing chap
ters, which, we believe, provide a comprehensive illustration of the robust
Bayesian approach. All the papers have been refereed by at least two people,
mainly chosen among the contributors; we wish to acknowledge the work by
Marek ME;czarski, Antonio Pievatolo, Pablo Arias, Bruno Betro, Alessandra
vi Preface
Guglielmi, Paul Gustafson, Juanmi Marin, Jacinto Martin, Elias Moreno,
Peter Miiller, Marco Perone Pacifico, Siva Sivaganesan, Cid Srinivasan,
Luca Tardella and Mike Wiper in refereeing the papers.
We are also grateful to John Kimmel for all his fruitful comments and
the Springer-Verlag referees for considering our proposal. Special thanks go
to our families Susana and Anna, Giacomo and Lorenzo and our parents
for their support and patience while preparing the volume.
David Rios Insua and Fabrizio Ruggeri
MOSTOLES AND MILANO
(EUROPEAN UNION)
APRIL 2000
Contents
Preface v
I Introduction
1 Bayesian Robustness 1
J. O. Berger, D. Rios Insua and F. Ruggeri
II Foundations
2 Topics on the Foundations of Robust Bayesian Analysis 33
D. Rios Insua and R. Criado
III Global and Local Robustness
3 Global Bayesian Robustness for Some Classes of Prior
Distributions 45
E. Moreno
4 Local Robustness in Bayesian Analysis 71
P. Gustafson
5 Global and Local Robustness Approaches: Uses and
Limitations 89
S. Sivaganesan
6 On the Use of the Concentration Function in Bayesian
Robustness 109
S. Fortini and F. Ruggeri
IV Likelihood Robustness
7 Likelihood Robustness 127
N.D. Shyamalkumar
viii Contents
V Loss Robustness
8 Ranges of Posterior Expected Losses and f-Robust
Actions 145
D. Dey and A. Micheas
9 Computing Efficient Sets in Bayesian Decision
Problems 161
J. Martin and J.P. Arias
10 Stability of Bayes Decisions and Applications 187
J. Kadane, G. Salinetti and C. Srinivasan
VI Comparison With Other
Statistical Methods
11 Robustness Issues in Bayesian Model Selection 197
B. Liseo
12 Bayesian Robustness and Bayesian Nonparametrics 223
S. Basu
13 f-Minimax: A Paradigm for Conservative Robust
Bayesians 241
B. Vidakovic
VII Algorithms
14 Linearization Techniques in Bayesian Robustness 261
M. Lavine, M. Perone Pacifico, G. Salinetti and L. Tardella
15 Methods for Global Prior Robustness under
Generalized Moment Conditions 273
B. Betro and A. Guglielmi
16 Efficient MCMC Schemes for Robust Model Extensions
Using Encompassing Dirichlet Process Mixture Models 295
S. MacEachern and P. Muller
VIII Case Studies
17 Sensitivity Analysis in IctNeo 317
C. Bielza, S. Rios Insua, M. Gomez and J.A. Fernandez del Pozo
Contents IX
18 Sensitivity of Replacement Priorities for Gas Pipeline
Maintenance 335
E. Cagno, F. Caron, M. Mancini and F. Ruggeri
19 Robust Bayesian Analysis in Medical
and Epidemiological Settings 351
B.P. Carlin and M.E. Perez
20 A Robust Version of the Dynamic Linear Model
with an Economic Application 373
J.M. Marin
21 Prior Robustness in Some Common Types of Software
Reliability Model 385
S.P. Wilson and M.P. Wiper
Bibliography 401
Contributors
Pablo Arias, [email protected], Departamento de Matematicas, Escuela
Politecnica de Caceres, Universidad de Extremadura, Caceres, Spain.
Sanjib Basu, [email protected], Division of Statistics, Northern Illinois
University, DeKalb, IL, USA.
James O. Berger, [email protected], Institute of Statistics and Deci
sion Sciences, Duke University, Durham, NC, USA.
Bruno Betro, [email protected], Consiglio Nazionale delle Ricerche,
Istituto per Ie Applicazioni della Matematica e dell'lnformatica, Mi
lano, Italy.
Concha Bielza, [email protected], Departamento de Inteligencia Arti
ficial, U niversidad Politecnica de Madrid, Boadilla del Monte, Madrid,
Spain.
Enrico Cagno, Enrico. [email protected], Politecnico di Milano, Diparti
mento di Meccanica, Milano, Italy.
Bradley P. Carlin, [email protected], Division of Biostatistics, School
of Public Health, University of Minnesota, Minneapolis, MN, USA.
Franco Caron, Franco. [email protected], Politecnico di Milano, Diparti
mento di Meccanica, Milano, Italy.
Regina Criado, [email protected], Department of Experimental Sci
ences and Engineering, Universidad Rey Juan Carlos, Mostoles, Mad
rid, Spain.
Dipak K. Dey, [email protected], Department of Statistics, University
of Connecticut, Storrs, CT, USA.
Juan A. Fernandez del Pozo, [email protected], Departamento de
Inteligencia Artificial, Universidad Politecnica de Madrid, Boadilla
del Monte, Madrid, Spain.
Sandra Fortini, [email protected], Istituto di Metodi Quan
titativi, Universita "L. Bocconi", Milano, Italy.
Manuel Gomez, [email protected], Departamento de Inteligencia Arti
ficial, Universidad Politecnica de Madrid, Boadilla del Monte, Madrid,
Spain.