Frontiers of Statistical Decision Makingand Bayesian Analysis

Ming-Hui Chen · Dipak K. Dey · Peter Muller ·Dongchu Sun · Keying YeEditors

Frontiers of StatisticalDecision Makingand Bayesian Analysis

In Honor of James O. Berger

123

EditorsProf. Ming-Hui ChenDepartment of StatisticsUniversity of Connecticut215 Glenbrook Road, U-4120Storrs, CT 06269USAmhchen@stat.uconn.edu

Prof. Dipak K. DeyDepartment of StatisticsUniversity of Connecticut215 Glenbrook Road, U-4120Storrs, CT 06269USAdipak.dey@uconn.edu

Prof. Peter MullerDepartment of BiostatisticsThe University of TexasM. D. Anderson Cancer Center1515 Holcombe Boulevard, Box 447Houston, TX 77030USApmueller@mdanderson.org

Prof. Dongchu SunDepartment of StatisticsUniversity of Missouri-Columbia146 Middlebush HallColumbia, MO 65211USAsund@missouri.edu

Prof. Keying YeDepartment of Management Scienceand Statistics, College of BusinessUniversity of Texas at San AntonioSan Antonio, TX 78249USAKeying.Ye@utsa.edu

ISBN 978-1-4419-6943-9 e-ISBN 978-1-4419-6944-6DOI 10.1007/978-1-4419-6944-6Springer New York Dordrecht Heidelberg London

Library of Congress Control Number: 2010931142

c© Springer Science+Business Media, LLC 2010All rights reserved. This work may not be translated or copied in whole or in part without the writtenpermission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York,NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use inconnection with any form of information storage and retrieval, electronic adaptation, computersoftware, or by similar or dissimilar methodology now known or hereafter developed is forbidden.The use in this publication of trade names, trademarks, service marks, and similar terms, even ifthey are not identified as such, is not to be taken as an expression of opinion as to whether or notthey are subject to proprietary rights.

Printed on acid-free paper

Springer is part of Springer Science+Business Media (www.springer.com)

Dedicated to Jim and Ann Berger for their encouragement, supportand love all through our academic life and beyond

Preface

This book surveys the current research frontiers in Bayesian statistics. Over thelast decades we have seen an unprecedented explosion of exciting Bayesian work.The explosion is in sheer number of researchers and publications, as well as in thediversity of application areas and research directions. Over the past few years sev-eral excellent new introductory texts on Bayesian inference have appeared, as wellas specialized monographs that focus on specific aspects of Bayesian inference, in-cluding dynamic models, multilevel data, non-parametric Bayes, bioinformatics andmany others. Thus this is a natural time for a book that can pull all these diverse areastogether and present a snapshot of current research frontiers in Bayesian inferenceand decision making. The intention of this volume is to provide such a snapshot.

Many of the research frontiers that are discussed in this volume have a closeconnection to the life and career of Jim Berger, thus the subtitle of this book. Notcoincidentally, many authors are former students, collaborators, and friends of JimBerger. Like few others Jim has been instrumental in shaping the recent expansionof Bayesian research. Jim’s early work in admissibility, shrinkage estimation, andon conditioning established some of the foundations that current work builds on.Working on admissibility naturally leads to later work on robustness, an issue thatis again becoming a paramount concern as we move to increasingly more complexmodels. Work on robustness and admissibility also reflects Jim’s lifelong interestin the Bayesian-frequentist interface. This interest led him to study Bayesian p-values and objective Bayes methodology, two other important research directionsin Jim’s work. Reflecting a general trend in Bayesian statistics research, Jim alsobecame increasingly involved with substantial applications and practical aspects ofBayesian inference, starting with work on fuel efficiency in the 90’s, and continuingwith work on astronomy, computer experiments, and more.

Besides his own research, Jim’s close association with Bayesian research andstatistics research in general arises from his long record of service in the profes-sion, including serving as president of IMS, ISBA and ASA/SBSS, as co-editor ofthe Annals of Statistics and as organizer of countless conferences and as a memberof the US National Academy of Science as well as the Spanish Real Academia deCiencias. Over the last eight years Jim has shaped statistics research also by his

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leadership as the founding director for the new Statistical and Applied Mathemati-cal Sciences Institute (SAMSI). Many researchers who participated in the excitingprograms at SAMSI over the last 10 years greatly appreciate Jim’s hard work tocreate and maintain the unique research environment at SAMSI. Most importantlyto us and many authors of the chapters in this volume, Jim has substantially con-tributed to the development of statistics research as an outstanding advisor, mentorand colleague. Jim has been advisor to over 30 Ph.D. students. We truly appreciatethe privilege of Jim’s guidance and help, which often went way beyond our yearsas graduate students. Here we need to also acknowledge Ann Berger as the superlurking variable behind Jim’s extraordinary career and the success of many of hisstudents. Thanks!

The chapters in this book were chosen to provide a broad survey of current re-search frontiers in Bayesian analysis, ranging from foundations, to methodologyissues, to computational themes and applications. It is an amazing feature of Jim’slife and research that the chapters in this book happen to simultaneously also almostbe an inventory of his many research interests.

Ming-Hui Chen, Dipak K. Dey, Peter Muller,March 2010 Dongchu Sun, and Keying Ye

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Biography of James O. Berger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 The Frontiers of Research at SAMSI . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2.1 Research Topics from Past SAMSI Programs . . . . . . . . . . . . . 31.2.2 Research Topics from Current SAMSI Programs . . . . . . . . . . 221.2.3 Research Topics in Future Programs . . . . . . . . . . . . . . . . . . . . 24

1.3 Overview of the Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2 Objective Bayesian Inference with Applications . . . . . . . . . . . . . . . . . . . 312.1 Bayesian Reference Analysis of the Hardy-Weinberg Equilibrium

Jose M. Bernardo and Vera Tomazella . . . . . . . . . . . . . . . . . . . . . . . . . 312.1.1 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322.1.2 Objective Precise Bayesian Testing . . . . . . . . . . . . . . . . . . . . . 332.1.3 Testing for Hardy-Weinberg Equilibrium . . . . . . . . . . . . . . . . 352.1.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

2.2 Approximate Reference Priors in the Presence of Latent StructureBrunero Liseo, Andrea Tancredi, and Maria M. Barbieri . . . . . . . . . . 442.2.1 The Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452.2.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 472.2.3 The Case with Nuisance Parameters . . . . . . . . . . . . . . . . . . . . 532.2.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

2.3 Reference Priors for Empirical LikelihoodsBertrand Clarke and Ao Yuan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 562.3.1 Empirical Likelihood . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 572.3.2 Reference Priors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 582.3.3 Relative Entropy Reference Priors . . . . . . . . . . . . . . . . . . . . . . 612.3.4 Hellinger Reference Prior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 652.3.5 Chi-square Reference Prior . . . . . . . . . . . . . . . . . . . . . . . . . . . . 662.3.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

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3 Bayesian Decision Based Estimation and Predictive Inference . . . . . . . 693.1 Bayesian Shrinkage Estimation

William E. Strawderman. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 693.1.1 Some Intuition into Shrinkage Estimation . . . . . . . . . . . . . . . . 703.1.2 Some Theory for the Normal Case with Covariance σ2I . . . . 723.1.3 Results for Known Σ and General Quadratic Loss . . . . . . . . . 773.1.4 Conclusion and Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

3.2 Bayesian Predictive Density EstimationEdward I. George and Xinyi Xu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 833.2.1 Prediction for the Multivariate Normal Distribution . . . . . . . . 853.2.2 Predictive Density Estimation for Linear Regression . . . . . . . 883.2.3 Multiple Shrinkage Predictive Density Estimation . . . . . . . . . 903.2.4 Simulation Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 913.2.5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

3.3 Automated Bias-variance Trade-off: Intuitive Inadmissibility orInadmissible Intuition?Xiao-Li Meng . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 953.3.1 Always a Good Question ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . 963.3.2 Gene-Environment Interaction and a Misguided Insight . . . . 973.3.3 Understanding Partially Bayes Methods . . . . . . . . . . . . . . . . . 1003.3.4 Completing M&C’s Argument . . . . . . . . . . . . . . . . . . . . . . . . . 1033.3.5 Learning through Exam: The Actual Qualifying Exam

Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1053.3.6 Interweaving Research and Pedagogy: The Actual

Annotated Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1073.3.7 A Piece of Inadmissible Cake? . . . . . . . . . . . . . . . . . . . . . . . . . 111

4 Bayesian Model Selection and Hypothesis Tests . . . . . . . . . . . . . . . . . . . . 1134.1 Performance of Bayesian Model Selection Criteria for Gaussian

Mixture ModelsRussell J. Steele and Adrian E. Raftery . . . . . . . . . . . . . . . . . . . . . . . . 1134.1.1 Bayesian Model Selection for Mixture Models . . . . . . . . . . . . 1144.1.2 A Unit Information Prior for Mixture Models . . . . . . . . . . . . . 1184.1.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1224.1.4 Simulation Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1254.1.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

4.2 How Large Should the Training Sample Be?Luis Pericchi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1304.2.1 General Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1314.2.2 An Exact Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1354.2.3 Discussion of the FivePercent-Cubic-Root Rule . . . . . . . . . . . 142

4.3 A Conservative Property of Bayesian Hypothesis TestsValen E. Johnson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1424.3.1 An Inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1434.3.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

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4.4 An Assessment of the Performance of Bayesian Model Averagingin the Linear ModelIlya Lipkovich, Keying Ye, and Eric P. Smith . . . . . . . . . . . . . . . . . . . 1464.4.1 Assessment of BMA Performance . . . . . . . . . . . . . . . . . . . . . . 1484.4.2 A Simulation Study of BMA Performance . . . . . . . . . . . . . . . 1494.4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

5 Bayesian Inference for Complex Computer Models . . . . . . . . . . . . . . . . 1575.1 A Methodological Review of Computer Models

M.J. Bayarri . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1575.1.1 Computer Models and Emulators . . . . . . . . . . . . . . . . . . . . . . . 1585.1.2 The Discrepancy (Bias) Function . . . . . . . . . . . . . . . . . . . . . . . 1595.1.3 Confounding of Tuning and Bias . . . . . . . . . . . . . . . . . . . . . . . 1635.1.4 Modularization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1645.1.5 Additional Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1675.1.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168

5.2 Computer Model Calibration with Multivariate Spatial OutputK. Sham Bhat, Murali Haran, and Marlos Goes . . . . . . . . . . . . . . . . . . 1685.2.1 Computer Model Calibration with Spatial Output . . . . . . . . . 1705.2.2 Calibration with Multivariate Spatial Output . . . . . . . . . . . . . 1725.2.3 Application to Climate Parameter Inference . . . . . . . . . . . . . . 1765.2.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1795.2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

6 Bayesian Nonparametrics and Semi-parametrics . . . . . . . . . . . . . . . . . . 1856.1 Bayesian Nonparametric Goodness of Fit Tests

Surya T. Tokdar, Arijit Chakrabarti, and Jayanta K. Ghosh . . . . . . . . 1856.1.1 An Early Application of Bayesian Ideas in Goodness of

Fit Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1876.1.2 Testing a Point Null versus Non-parametric Alternatives . . . 1876.1.3 Posterior Consistency for a Composite Goodness of Fit Test 1896.1.4 Bayesian Goodness of Fit Tests . . . . . . . . . . . . . . . . . . . . . . . . 192

6.2 Species Sampling Model and Its Application to Bayesian StatisticsJaeyong Lee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1946.2.1 Basic Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1966.2.2 Construction Methods for EPPFs . . . . . . . . . . . . . . . . . . . . . . . 2016.2.3 Statistical Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2046.2.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206

6.3 Hierarchical Models, Nested Models, and Completely RandomMeasuresMichael I. Jordan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2076.3.1 Completely Random Measures . . . . . . . . . . . . . . . . . . . . . . . . . 2086.3.2 Marginal Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2106.3.3 Hierarchical Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2126.3.4 Nested Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214

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6.3.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216

7 Bayesian Influence and Frequentist Interface . . . . . . . . . . . . . . . . . . . . . . 2197.1 Bayesian Influence Methods

Hongtu Zhu, Joseph G. Ibrahim, Hyunsoon Cho, and NianshengTang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219

7.1.1 Bayesian Case Influence Measures . . . . . . . . . . . . . . . . . . . . . . 2217.1.2 Bayesian Global and Local Robustness . . . . . . . . . . . . . . . . . . 2267.1.3 An Illustrative Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233

7.2 The Choice of Nonsubjective Priors on Hyperparameters forHierarchical Bayes ModelsGauri S. Datta and J.N.K. Rao . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2377.2.1 Probability Matching in Small Area Estimation . . . . . . . . . . . 2407.2.2 Frequentist Evaluation of Posterior Variance . . . . . . . . . . . . . 2427.2.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245

7.3 Exact Matching Inference for a Multivariate Normal ModelLuyan Dai and Dongchu Sun . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2477.3.1 The Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2497.3.2 Main Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252

8 Bayesian Clinical Trials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2578.1 Application of a Bayesian Doubly Optimal Group Sequential

Design for Clinical TrialsJ. Kyle Wathen and Peter F. Thall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2578.1.1 A Non-Small Cell Lung Cancer Trial . . . . . . . . . . . . . . . . . . . . 2578.1.2 Bayesian Doubly Optimal Group Sequential Designs . . . . . . 2598.1.3 Application of BDOGS to the Lung Cancer Trial . . . . . . . . . . 2628.1.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269

8.2 Experimental Design and Sample Size Computations forLongitudinal ModelsRobert E. Weiss and Yan Wang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2708.2.1 Covariates and Missing Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 2718.2.2 Simulating the Predictive Distributions of the Bayes Factor . 2718.2.3 Sample Size for a New Repeated Measures Pediatric Pain

Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2728.3 A Bayes Rule for Subgroup Reporting

Peter Muller, Siva Sivaganesan, and Purushottam W. Laud . . . . . . . . 2778.3.1 The Model Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2778.3.2 Subgroup Selection as a Decision Problem . . . . . . . . . . . . . . . 2788.3.3 Probability Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2818.3.4 A Dementia Trial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2828.3.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284

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9 Bayesian Methods for Genomics, Molecular and Systems Biology . . . . 2859.1 Bayesian Modelling for Biological Annotation of Gene

Expression Pathway SignaturesHaige Shen and Mike West . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2859.1.1 Context and Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2879.1.2 Computation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2909.1.3 Evaluation and Illustrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2939.1.4 Applications to Hormonal Pathways in Breast Cancer . . . . . . 2969.1.5 Theoretical and Algorithmic Details . . . . . . . . . . . . . . . . . . . . 3009.1.6 Summary Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302

9.2 Bayesian Methods for Network-Structured Genomics DataStefano Monni and Hongzhe Li . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3039.2.1 Bayesian Variable Selection with a Markov Random Field

Prior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3049.2.2 Numerical Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3099.2.3 Discussion and Future Direction . . . . . . . . . . . . . . . . . . . . . . . . 315

9.3 Bayesian PhylogeneticsErik W. Bloomquist and Marc A. Suchard . . . . . . . . . . . . . . . . . . . . . . 3169.3.1 Statistical Phyloalignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3199.3.2 Multilocus Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3219.3.3 Looking Ahead . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324

10 Bayesian Data Mining and Machine Learning . . . . . . . . . . . . . . . . . . . . . 32710.1 Bayesian Model-based Principal Component Analysis

Bani K. Mallick, Shubhankar Ray, and Soma Dhavala . . . . . . . . . . . . 32710.1.1 Random Principal Components . . . . . . . . . . . . . . . . . . . . . . . . 32910.1.2 Piecewise RPC Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33110.1.3 Principal Components Clustering . . . . . . . . . . . . . . . . . . . . . . . 33410.1.4 Reversible Jump Proposals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33710.1.5 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340

10.2 Priors on the Variance in Sparse Bayesian Learning: thedemi-Bayesian LassoSuhrid Balakrishnan and David Madigan . . . . . . . . . . . . . . . . . . . . . . . 34610.2.1 Background and Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34710.2.2 The demi-Bayesian Lasso . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35010.2.3 Experiments and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35410.2.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359

10.3 Hierarchical Bayesian Mixed-Membership Models and LatentPattern DiscoveryEdoardo M. Airoldi, Stephen E. Fienberg, Cyrille J. Joutard, and

Tanzy M. Love . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36010.3.1 Characterizing HBMM Models . . . . . . . . . . . . . . . . . . . . . . . . 36310.3.2 Strategies for Model Choice . . . . . . . . . . . . . . . . . . . . . . . . . . . 36410.3.3 Case Study: PNAS 1997–2001 . . . . . . . . . . . . . . . . . . . . . . . . . 36510.3.4 Case Study: Disability Profiles . . . . . . . . . . . . . . . . . . . . . . . . . 369

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10.3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374

11 Bayesian Inference in Political Science, Finance, and MarketingResearch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37711.1 Prior Distributions for Bayesian Data Analysis in Political Science

Andrew Gelman . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37711.1.1 Statistics in Political Science . . . . . . . . . . . . . . . . . . . . . . . . . . . 37811.1.2 Mixture Models and Different Ways of Encoding Prior

Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37911.1.3 Incorporating Extra Information Using Poststratification . . . 38011.1.4 Prior Distributions for Varying-Intercept, Varying-Slope

Multilevel Regressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38111.1.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382

11.2 Bayesian Computation in FinanceSatadru Hore, Michael Johannes, Hedibert Lopes, Robert E.

McCulloch, and Nicholas G. Polson . . . . . . . . . . . . . . . . . . . . 38311.2.1 Empirical Bayesian Asset Pricing . . . . . . . . . . . . . . . . . . . . . . . 38411.2.2 Bayesian Inference via SMC . . . . . . . . . . . . . . . . . . . . . . . . . . . 38511.2.3 Bayesian Inference via MCMC. . . . . . . . . . . . . . . . . . . . . . . . . 38811.2.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396

11.3 Simulation-based-Estimation in Portfolio SelectionEric Jacquier and Nicholas G. Polson . . . . . . . . . . . . . . . . . . . . . . . . . . 39611.3.1 Basic Asset Allocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39811.3.2 Optimum Portfolios by MCMC . . . . . . . . . . . . . . . . . . . . . . . . 40511.3.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409

11.4 Bayesian Multidimensional Scaling and Its Applications inMarketing ResearchDuncan K.H. Fong . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41011.4.1 Bayesian Vector MDS Models . . . . . . . . . . . . . . . . . . . . . . . . . 41211.4.2 A Marketing Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41411.4.3 Discussion and Future Research . . . . . . . . . . . . . . . . . . . . . . . . 416

12 Bayesian Categorical Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41912.1 Good Smoothing

James H. Albert . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41912.1.1 Good’s 1967 Paper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42012.1.2 Examples of Good Smoothing . . . . . . . . . . . . . . . . . . . . . . . . . 42612.1.3 Smoothing Hitting Rates in Baseball . . . . . . . . . . . . . . . . . . . . 43012.1.4 Closing Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435

12.2 Bayesian Analysis of Matched Pair DataMalay Ghosh and Bhramar Mukherjee . . . . . . . . . . . . . . . . . . . . . . . . . 43612.2.1 Item Response Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43712.2.2 Bayesian Analysis of Matched Case-Control Data . . . . . . . . . 43912.2.3 Some Equivalence Results in Matched Case-Control Studies 44512.2.4 Other Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 448

Contents xv

12.2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44912.3 Bayesian Choice of Links and Computation for Binary Response

DataMing-Hui Chen, Sungduk Kim, Lynn Kuo, and Wangang Xie . . . . . 45112.3.1 The Binary Regression Models . . . . . . . . . . . . . . . . . . . . . . . . . 45312.3.2 Prior and Posterior Distributions . . . . . . . . . . . . . . . . . . . . . . . 45412.3.3 Computational Development . . . . . . . . . . . . . . . . . . . . . . . . . . . 45612.3.4 A Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46112.3.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464

13 Bayesian Geophysical, Spatial and Temporal Statistics . . . . . . . . . . . . . 46713.1 Modeling Spatial Gradients on Response Surfaces

Sudipto Banerjee and Alan E. Gelfand . . . . . . . . . . . . . . . . . . . . . . . . . 46713.1.1 Directional Derivative Processes . . . . . . . . . . . . . . . . . . . . . . . 46913.1.2 Mean Surface Gradients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47113.1.3 Posterior Inference for Gradients . . . . . . . . . . . . . . . . . . . . . . . 47313.1.4 Gradients under Spatial Dirichlet Processes . . . . . . . . . . . . . . 47513.1.5 Illustration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47713.1.6 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483

13.2 Non-Gaussian Hierarchical Generalized Linear GeostatisticalModel SelectionXia Wang, Dipak K. Dey, and Sudipto Banerjee . . . . . . . . . . . . . . . . . 48413.2.1 A Review on the Generalized Linear Geostatistical Model . . 48613.2.2 Generalized Extreme Value Link Model . . . . . . . . . . . . . . . . . 48713.2.3 Prior and Posterior Distributions for the GLGM Model

under Different Links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48913.2.4 A Simulated Data Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49013.2.5 Analysis of Celastrus Orbiculatus Data . . . . . . . . . . . . . . . . . . 49213.2.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 496

13.3 Objective Bayesian Analysis for Gaussian Random FieldsVictor De Oliveira . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49713.3.1 Gaussian Random Field Models . . . . . . . . . . . . . . . . . . . . . . . . 49813.3.2 Integrated Likelihoods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49913.3.3 Reference Priors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50013.3.4 Jeffreys Priors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50313.3.5 Other Spatial Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50513.3.6 Further Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50713.3.7 Multi-Parameter Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50813.3.8 Discussion and Some Open Problems . . . . . . . . . . . . . . . . . . . 511

14 Posterior Simulation and Monte Carlo Methods . . . . . . . . . . . . . . . . . . . 51314.1 Importance Sampling Methods for Bayesian Discrimination

between Embedded ModelsJean-Michel Marin and Christian P. Robert . . . . . . . . . . . . . . . . . . . . . 51314.1.1 The Pima Indian Benchmark Model . . . . . . . . . . . . . . . . . . . . . 514

xvi Contents

14.1.2 The Basic Monte Carlo Solution . . . . . . . . . . . . . . . . . . . . . . . . 51714.1.3 Usual Importance Sampling Approximations . . . . . . . . . . . . . 51814.1.4 Bridge Sampling Methodology . . . . . . . . . . . . . . . . . . . . . . . . . 52014.1.5 Harmonic Mean Approximations . . . . . . . . . . . . . . . . . . . . . . . 52314.1.6 Exploiting Functional Equalities . . . . . . . . . . . . . . . . . . . . . . . . 52514.1.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527

14.2 Bayesian Computation and the Linear ModelMatthew J. Heaton and James G. Scott . . . . . . . . . . . . . . . . . . . . . . . . . 52714.2.1 Bayesian Linear Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52914.2.2 Algorithms for Variable Selection and Shrinkage . . . . . . . . . . 53114.2.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53714.2.4 Final Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545

14.3 MCMC for Constrained Parameter and Sample SpacesMerrill W. Liechty, John C. Liechty, and Peter Muller . . . . . . . . . . . . 54514.3.1 The Shadow Prior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54714.3.2 Example: Modeling Correlation Matrices . . . . . . . . . . . . . . . . 54914.3.3 Simulation Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55014.3.4 Classes of Models Suitable for Shadow Prior Augmentations 55114.3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 552

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555

Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 615

Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 627

List of Contributors

Edoardo M. AiroldiDepartment of StatisticsHarvard UniversityScience Center1 Oxford StreetCambridge, MA 02138-2901, USAe-mail: airoldi@fas.harvard.edu

James H. AlbertDepartment of Mathematicsand StatisticsBowling Green State UniversityBowling Green, Ohio 43403, USAe-mail: albert@math.bgsu.eduand e-mail: albertcb1@gmail.com

Sudipto BanerjeeDivision of BiostatisticsSchool of Public HealthUniversity of Minnesota420 Delaware Street SEA460 Mayo Bldg. MMC 303Minneapolis, MN 55455, USAe-mail: baner009@umn.edu

Suhrid BalakrishnanAT&T Labs Research180 Park AvenueFlorham Park, NJ 07932, USAe-mail: suhrid@research.att.com

Maria M. BarbieriDipartimento di EconomiaUniversita Roma Trevia Silvio D’Amico, 7700145 Roma, ITALYe-mail: barbieri@uniroma3.it

Susie M.J. BayarriDepartment of Statistics and O.R.University of ValenciaDr. Moliner 5046100 Burjassot, Valencia, Spaine-mail: Susie.Bayarri@uv.es

Jose M. BernardoDepartment of Statistics and O.R.University of ValenciaDr. Moliner 5046100 Burjassot, Valencia, Spaine-mail: jose.m.bernardo@uv.es

K. Sham BhatDepartment of StatisticsPennsylvania State University326 Thomas BuildingUniversity Park, PA 16802, USAe-mail: kgb130@psu.edu

Erik W. BloomquistMathematical Biosciences InstituteThe Ohio State University381 Jennings Hall

xvii

xviii List of Contributors

1735 Neil AvenueColumbus, OH 43210, USAe-mail: bloomquist.2@osu.edu

Arijit ChakrabartiBayesian and InterdisciplinaryResearch UnitIndian Statistical InstituteKolkata - 700108, West Bengal, Indiae-mail: arc@isical.ac.in

Ming-Hui ChenDepartment of StatisticsUniversity of Connecticut215 Glenbrook Road, U-4120Storrs, CT 06269, USAe-mail: mhchen@stat.uconn.edu

Hyunsoon ChoNational Cancer Institute6116 Executive Boulevard Suite 504Bethesda, MD 20892, USAe-mail: choh3@mail.nih.gov

Bertrand ClarkeDepartment of MedicineCenter for Computational Sciencesand Department of Epidemiologyand Public HealthUniversity of Miami1120 NW 14th StreetCRB 611 (C-213)Miami, FL, 33136, USAe-mail: bclarke2@med.miami.edu

Luyan DaiBoehringer Ingelheim Pharm Inc.CC G2225A900 Ridgebury RoadRidgefield, CT 06877, USAe-mail: luyan.dai@boehringer-ingelheim.com

Gauri S. DattaDepartment of StatisticsUniversity of GeorgiaAthens, GA 30602-1952, USAe-mail: gaurisdatta@gmail.com

Victor De OliveiraDepartment of Management Scienceand StatisticsThe University of Texas at San AntonioOne UTSA CircleSan Antonio, TX 78249, USAe-mail: Victor.DeOliveira@utsa.edu

Dipak K. DeyDepartment of StatisticsUniversity of Connecticut215 Glenbrook Road, U-4120Storrs, CT 06269, USAe-mail: dipak.dey@uconn.edu

Soma DhavalaStatistics DepartmentTexas A&M UniversityCollege Station, TX 77843-3143 USAe-mail: soma@stat.tamu.edu

Stephen E. Fienberg132G Baker HallDepartment of StatisticsCarnegie Mellon UniversityPittsburgh, PA 15213-3890, USAe-mail: fienberg@stat.cmu.edu

Duncan K.H. FongDepartment of MarketingSmeal College of Business456 Business BuildingPenn State UniversityUniversity Park, PA 16802, USAe-mail: i2v@psu.edu

Alan E. GelfandDepartment of Statistical ScienceDuke UniversityDurham, NC 27708-0251, USAe-mail: alan@stat.duke.edu

Andrew GelmanDepartment of Statistics1255 Amsterdam Ave, room 1016Department of Political ScienceInternational Affairs Bldg, room 731Columbia University

List of Contributors xix

New York, N.Y. 10027, USAe-mail: gelman@stat.columbia.edu

Edward I. GeorgeDepartment of StatisticsThe Wharton SchoolUniversity of PennsylvaniaPhiladelphia, PA 19104-6302, USAe-mail: edgeorge@wharton.upenn.edu

Jayanta K. GhoshDepartment of StatisticsPurdue University250 N. University StreetWest Lafayette, IN 47907-2066, USAe-mail: ghosh@stat.purdue.edu

Malay GhoshDepartment of StatisticsUniversity of Florida102 Griffin-Floyd HallP.O. Box 118545Gainesville, Florida 32611, USAe-mail: ghoshm@stat.ufl.edu

Marlos GoesASA - South AmericaRua Fidalga, 711Sao Paulo, Brazil 05432-070e-mail: mpg14@psu.edu

Murali HaranDepartment of StatisticsPennsylvania State University326 Thomas BuildingUniversity Park, PA 16802, USAe-mail: mharan@stat.psu.edu

Matthew J. HeatonDepartment of Statistical ScienceDuke UniversityDurham, NC 27708-0251, USAe-mail: matt@stat.duke.edu

Satadru HoreFederal Reserve Bank of Boston600 Atlantic AvenueBoston, MA 02210, USAe-mail: satadru.hore@gmail.com

Joseph G. IbrahimDepartment of BiostatisticsUniversity of North CarolinaMcGavran-Greenberg HallChapel Hill, NC 27599, USAe-mail: ibrahim@bios.unc.edu

Eric Jacquier3000 chemin de la Cote-Sainte-CatherineFinance DepartmentCIRANO and HEC. MontrealMontreal, QC H3T 2A7, Canadae-mail: eric.jacquier@hec.ca

Michael JohannesGraduate School of BusinessColumbia University3022 Broadway, Uris Hall 424New York, NY 10027, USAe-mail: mj335@columbia.edu

Valen E. JohnsonDepartment of BiostatisticsThe University of TexasM. D. Anderson Cancer Center1515 Holcombe Boulevard, Box 447Houston, TX 77030, USAe-mail: vejohnson@mdanderson.org

Michael I. Jordan427 Evans HallDepartment of Statisticsand Department of EECSUniversity of CaliforniaBerkeley, CA 94720-3860, USAe-mail: jordan@eecs.berkeley.edu

Cyrille J. JoutardDepartement de MathematiquesUniversite Montpellier 234095 Montpellier Cedex, Francee-mail: cjoutard@math.univ-montp2.fr

Sungduk KimDivision of Epidemiology,Statistics and Prevention ResearchEunice Kennedy Shriver National

xx List of Contributors

Institute of Child Healthand Human DevelopmentNIH, Rockville, MD 20852, USAe-mail: kims2@mail.nih.gov

Lynn KuoDepartment of StatisticsUniversity of Connecticut215 Glenbrook Road, U-4120Storrs, CT 06269-4120, USAe-mail: lynn@stat.uconn.edu

Purushottam W. LaudDivision of BiostatisticsMedical College of Wisconsin8701 Watertown Plank RoadMilwaukee, WI 53226, USAe-mail: laud@mcw.edu

Jaeyong LeeDepartment of StatisticsSeoul National UniversitySeoul 151-742, Koreae-mail: jylc@snu.ac.kr

Hongzhe LiDepartment of Biostatisticsand EpidemiologySchool of MedicineUniversity of Pennsylvania920 Blockley Hall423 Guardian DrivePhiladelphia, PA 19104-6021, USAe-mail: hongzhe@mail.med.upenn.edu

John C. LiechtyDepartment of MarketingSmeal College of Businessand Department of StatisticsPennsylvania State UniversityUniversity Park, PA 16803, USAe-mail: jcl12@psu.edu

Merrill W. LiechtyDepartment of Decision SciencesLeBow College of Business224 Academic BuildingDrexel University

Philadelphia, PA 19104, USAe-mail: merrill@drexel.edu

Ilya LipkovichEli Lilly and CompanyIndianapolis, IN 46285, USAe-mail: Lipkovich ilya a@lilly.com

Brunero LiseoDipartimento di studi geoeconomiciSapienza Universita di RomaViale del Castro Laurenziano, 900161 Rome, Italye-mail: brunero.liseo@uniroma1.itand e-mail: brunero.liseo@gmail.com

Hedibert LopesBooth School of BusinessUniversity of Chicago5807 South Woodlawn AvenueChicago, IL 60637, USAe-mail: hlopes@ChicagoBooth.edu

Tanzy M. LoveDepartment of Biostatistics andComputational BiologyUniversity of Rochester Medical Center601 Elmwood Avenue, Box 630Rochester, NY 14642, USAe-mail:Tanzy Love@urmc.rochester.edu

David MadiganDepartment of StatisticsColumbia University1255 Amsterdam Ave.New York, NY 10027, USAe-mail: madigan@stat.columbia.edu

Bani K. MallickStatistics DepartmentTexas A&M UniversityCollege Station, TX 77843-3143 USAe-mail: bmallick@stat.tamu.edu

Jean-Michel MarinInstitut de Mathematiques etModelisation de MontpellierUniversite Montpellier 2,

List of Contributors xxi

Case Courrier 5134095 Montpellier cedex 5, Francee-mail:Jean-Michel.Marin@univ-montp2.fr

Robert E. McCullochMcCombs School of BusinessUniversity of Texas at Austin1 University Station, B6500Austin, TX 78712-0212, USAe-mail: robert.mcculloch1@gmail.com

Xiao-Li MengDepartment of StatisticsHarvard UniversityScience Center1 Oxford StreetCambridge, MA 02138-2901, USAe-mail: meng@stat.harvard.edu

Stefano MonniDepartment of Public HealthWeill Cornell Medical College402 East 67th StreetNew York, NY 10065-6304, USAe-mail: stm2013@med.cornell.edu

Bhramar MukherjeeDepartment of BiostatisticsUniversity of MichiganAnn Arbor, MI 48109, USAe-mail: bhramar@umich.edu

Peter MullerDepartment of BiostatisticsThe University of TexasM. D. Anderson Cancer Center1515 Holcombe Boulevard, Box 447Houston, TX 77030, USAe-mail: pmueller@mdanderson.org

Luis Raul Pericchi GuerraDepartment of MathematicsUniversity of Puerto Rico at RioPiedras Campus, P.O. Box 23355San Juan 00931-3355, Puerto Ricoe-mail: lrpericchi@uprrp.edu ande-mail: luarpr@gmail.com

Nicholas G. PolsonBooth School of BusinessUniversity of Chicago5807 South Woodlawn AvenueChicago, IL 60637, USAe-mail: ngp@ChicagoBooth.edu

Adrian RafteryDepartment of StatisticsUniversity of WashingtonBox 354322Seattle, WA 98195-4322, USAe-mail: raftery@u.washington.edu

J.N.K. RaoSchool of Mathematics and StatisticsCarleton UniversityOttawa ON K1S 5B6, Canadae-mail: jrao@math.carleton.ca

Shubhankar RayBiometrics Research, RY 33-300Merck & Company, P.O. Box 2000Rahway, NJ 07065, USAe-mail: shubhankar ray@merck.com

Christian P. RobertCEREMADEUniversite Paris Dauphine75775 Paris, andCREST, INSEE, Paris, Francee-mail: xian@ceremade.dauphine.fr

James G. ScottDepartment of Information, Risk,and Operations ManagementUniversity of Texas at Austin1 University Station, B6500Austin, TX 78712, USAe-mail:james.scott@mccombs.utexas.edu

Haige ShenNovartis Oncology, Biometrics180 Park Ave, 104-2K11, Florham Park,NJ 07932, USAe-mail: haigeshen@yahoo.com

xxii List of Contributors

Siva SivaganesanDepartment of Mathematical SciencesUniversity of Cincinnati811-C Old ChemistryPO Box 210025Cincinnati, OH 45221-0025, USAe-mail: siva.sivaganesan@uc.edu

Eric P. SmithDepartment of StatisticsVirginia TechBlacksburg, VA 24061, USAe-mail: epsmith@vt.edu

Russell J. SteeleDepartment of Mathematics andStatisticsMcGill University805 Sherbrooke OuestMontreal, QC, Canada H3A 2K6e-mail: steele@math.mcgill.ca

William E. StrawdermanDepartment of Statistics561 Hill Center, Busch CampusRutgers UniversityPiscataway, NJ 08854-8019, USAe-mail: straw@stat.rutgers.edu

Marc A. SuchardDepartments of Biomathematics,Biostatistics and Human GeneticsDavid Geffen School of Medicineat UCLA, 6558 Gonda Building695 Charles E. Young Drive, SouthLos Angeles, CA 90095-1766, USAe-mail: msuchard@ucla.edu

Dongchu SunDepartment of StatisticsUniversity of Missouri-Columbia146 Middlebush HallColumbia, MO 65211, USAe-mail: sund@missouri.edu

Andrea TancrediDipartimento di studi geoeconomiciSapienza Universita di Roma

Viale del Castro Laurenziano, 900161 Rome, Italye-mail: andrea.tancredi@uniroma1.it

Niansheng TangDepartment of StatisticsYunnan UniversityKunming 650091, YunnanP. R. of Chinae-mail: nstang@ynu.edu.cn

Peter F. ThallDepartment of BiostatisticsThe University of TexasM. D. Anderson Cancer Center1515 Holcombe Boulevard, Box 447Houston, TX 77030, USAe-mail: rex@mdanderson.org

Surya T. TokdarDepartment of Statistical ScienceDuke UniversityDurham, NC 27708-0251, USAe-mail: st118@stat.duke.edu

Vera TomazellaDepartamento de EstatısticaUniversidade Federal de Sao CarlosRodovia Washington Luiz, Km 235Monjolinho, 13565-905 - Sao CarlosSP - Brasil - Caixa-Postal: 676e-mail: vera@power.ufscar.br

Xia WangNational Institute of Statistical Sciences19 T.W. Alexander DriveP. O. Box 14006Research Triangle Park, NC 27709,USAe-mail: xiawang.z@gmail.com

Yan WangCenter for Drug Evaluationand ResearchU.S. Food and Drug Administration10903 New Hampshire AvenueSilver Spring, MD 20993, USAe-mail: yanwang20@yahoo.com

List of Contributors xxiii

J. Kyle WathenDepartment of BiostatisticsThe University of TexasM. D. Anderson Cancer Center1515 Holcombe Boulevard, Box 447Houston, TX 77030, USAe-mail: jkwathen@mdanderson.org

Robert E. WeissDepartment of BiostatisticsUCLA School of Public HealthLos Angeles, CA 90095, USAe-mail: robweiss@ucla.edu

Mike WestDepartment of Statistical ScienceDuke UniversityDurham, NC 27708-0251, USAe-mail: mw@stat.duke.edu

Wangang XieAbbott Lab100 Abbott Park, R436/AP9A-2Abbott Park, IL 60064, USAe-mail: Wangang.Xie@abbott.com

Xinyi XuDepartment of Statistics

The Ohio State University1958 Neil AvenueColumbus, OH 43210-1247, USAe-mail: xinyi@stat.osu.edu

Keying YeDepartment of Management Scienceand Statistics, College of BusinessUniversity of Texas at San AntonioSan Antonio, TX 78249, USAe-mail: Keying.Ye@utsa.edu

Ao YuanStatistical Genetics andBioinformatics UnitNational Human Genome CenterHoward University2216 Sixth Street, N.W., Suite 206Washington, DC 20059, USAe-mail: ayuan@howard.edu

Hongtu ZhuDepartment of BiostatisticsUniversity of North CarolinaMcGavran-Greenberg HallChapel Hill, NC 27599, USAe-mail: hzhu@bios.unc.edu

Chapter 1Introduction

In the years since the 1985 publication of Statistical Decision Theory and BayesianAnalysis by James Berger, there has been an enormous increase in the use ofBayesian analysis and decision theory in statistics and science. The rapid expansionin the use of Bayesian methods is due in part to substantial advances in compu-tational and modeling techniques, and Bayesian methods are now central in manybranches of science. The aim of this book is to review current research frontiersin Bayesian analysis and decision theory. It is impossible to provide an exhaustivediscussion of all current research in Bayesian statistics, so the book instead sum-marizes current research frontiers by providing representative examples of researchchallenges chosen from a wide variety of areas.

In this first chapter, Section 1.1 is a short biography of James Berger. One ofthe many important aspects of James Berger’s contributions to statistics and appliedmathematics is his leadership of the Statistical and Applied Mathematical ScienceInstitute (SAMSI). The exciting research themes that defined SAMSI programs overthe last eight years are reviewed in Section 1.2. The last section of this chaptercontains an overview of the book.

1.1 Biography of James O. Berger

James Berger was born on April 6, 1950 in Minneapolis, Minnesota, to Orvis andThelma Berger. He received his PhD in Mathematics from Cornell University in1974, five years after he graduated from high school. He then joined the depart-ment of statistics at Purdue University, receiving tenure two years later, and waspromoted to full professor in 1980. In 1985, he became Richard M. Brumfield Dis-tinguish Professor of Statistics at Purdue University. Since 1997, he has been Artsand Science Distinguished Professor of Statistics at Duke University. Currently heis also the director of the Statistical and Applied Mathematical Science Institute(SAMSI), located in Research Triangle Park, North Carolina, USA.

M.-H. Chen et al. (eds.), Frontiers of Statistical Decision Making 1and Bayesian Analysis, DOI 10.1007/978-1-4419-6944-6 1,c© Springer Science+Business Media, LLC 2010

2 1 Introduction

Berger was president of the Institute of Mathematical Statistics from 1995 to1996, chair of the Section on Bayesian Statistical Science of the American Statis-tical Association in 1995, and president of the International Society for BayesianAnalysis during 2004. He has been involved with numerous editorial activities, in-cluding co-editorship of the Annals of Statistics (the landmark journal in the statis-tical society) during the period 1998–2000, and has organized or participated in theorganization of over 39 conferences, including the Purdue Symposiums on Statisti-cal Decision Theory and Related Topics and the Valencia International Meetings onBayesian Statistics. He has also served on numerous statistical administrative andprogram committees, including the Committee on Applied and Theoretical Statis-tics of the National Research Council. Berger has also been on various universityand NSF site visit teams and panels, and NSF advisory committees.

Among the awards and honors Berger has received are Guggenheim and SloanFellowships, the 1985 COPSS President’s Award (an award given to a researcherno more than 40, in recognition of outstanding contributions to the statistics pro-fession), the Sigma Xi Research Award at Purdue University for contribution of theyear to science in 1993, the Fisher Lectureship in 2001, election as foreign memberof the Spanish Real Academia de Ciencias in 2002, election to the U.S. NationalAcademy of Sciences in 2003, award of an honorary Doctor of Science degree fromPurdue University in 2004, and the Wald Lectureship in 2007.

Berger’s research has primarily been in Bayesian statistics, foundations of statis-tics, statistical decision theory, simulation, model selection, and various interdis-ciplinary areas of science and industry, especially astronomy and the interface be-tween computer modeling and statistics. He has supervised over 30 PhD disserta-tions, published over 170 articles, and has written or edited 14 books or specialvolumes.

Berger married Ann Louise Duer (whom he first met when they were in the sev-enth grade together) in 1970, and they have two children, Jill Berger who is marriedto Sascha Hallstein and works as optical scientist in Silicon Valley, and Julie Gishwho is married to Ryan Gish and works as a consultant in Chicago. The Berger’shave three grandchildren, Charles and Alexander Gish and Sophia Hallstein.

1.2 The Frontiers of Research at SAMSI

James Berger was the founding Director of the Statistical and Applied Mathemat-ical Sciences Institute (SAMSI, http://www.samsi.info) in 2002. Created as part ofthe Mathematical Sciences Institutes program at the National Science Foundation,SAMSI’s vision is to forge a new synthesis of the statistical sciences and the ap-plied mathematical sciences with disciplinary science to confront the very hardestand most important data- and model-driven scientific challenges. Each year, morethan 100 researchers have participated in SAMSI research working groups throughextended visits, and SAMSI workshops have drawn over 1000 national and interna-tional participants annually.

1.2 The Frontiers of Research at SAMSI 3

In over eight years of stewardship of SAMSI, Berger has overseen the develop-ment and implementation of 24 major scientific programs (see http://www.samsi.info/programs/index.shtml), with others still under development. These programs pro-vide a snapshot of the views of Berger and other leaders in the statistical communityconcerning which topics are of central importance to statistics and its interactionwith other disciplines. We can thus summarize this view of the frontiers of statisticsby briefly reviewing the past, current, and future programs of SAMSI. Details ofeach of the programs and references can be found at the SAMSI website.

1.2.1 Research Topics from Past SAMSI Programs

1.2.1.1 Stochastic Computation, 2002–2003

Stochastic computation explored the use of methods of stochastic computation inthe following key areas of statistical modeling:

Stochastic computation in problems of model and variable selection: (i) com-puting hard likelihoods and Bayes’ factors for model comparison and selection; and(ii) synthesis of existing stochastic computational approaches to model uncertaintyand selection.

Stochastic computation in inference and imputation in contingency tables anal-ysis: (i) perfect simulation approaches to “missing data” problems; (ii) synthesisof existing Markov chain simulation methods — “local” and “global” move ap-proaches; (iii) experiments with approaches in large, sparse tables; and (iv) applica-tions in genetics and other areas.

Stochastic computation in analysis of large-scale graphical models: (i) MonteCarlo and related stochastic search methods for sparse, large-scale graphical models;(ii) model definition and specification for sparse models; and (iii) applications ingenomics (large-scale gene expression studies).

Stochastic computation in financial mathematics, especially in options pricingmodels: (i) Monte Carlo methods in specific options pricing models; and (ii) se-quential Monte Carlo methods and particle filtering in stochastic volatility models.

The core research focuses included studies of the performance characteristics ofcurrent stochastic computational methods, refinements and extensions of existingapproaches, and development of innovative new approaches. In two of the areas, inparticular, there was an explicit focus on the development of interactions betweenstatisticians (coming from methodological and applied perspectives) and theoreti-cal probabilists and mathematicians working on related problems. One key examplewas the component on imputation in contingency tables, with an interest in con-necting Markov chain methods from statistics with perfect sampling from probabil-ity and algebraic approaches from mathematics. Another example was in modeling

4 1 Introduction

in financial pricing studies where statistical and mathematical “schools” have hadlimited interactions.

1.2.1.2 Inverse Problem Methodology in Complex Stochastic Models,2002–2003

In a diverse range of fields, including engineering, biology, physical sciences, ma-terial sciences, and medicine, there is heightening interest in the use of complexdynamical systems to characterize underlying features of physical and biologicalprocesses. For example, a critical problem in the study of HIV disease is elucida-tion of mechanisms governing the evolution of patient resistance to antiretroviraltherapy, and there is growing consensus that progress may be made by representingthe interaction between virus and host immune system by nonlinear dynamical sys-tems whose parameters describe these mechanisms. Similarly, recovery of molec-ular information for polymers via light beam interrogation may be characterizedby a dynamical system approach. Risk assessment is increasingly focused on deriv-ing insights from physiologically based pharmacokinetic dynamical systems modelsdescribing underlying processes following exposure to potential carcinogens.

In all of these applications, a main objective is to use complex systems to uncoversuch mechanisms based on experimental findings; that is, in applied mathematicalparlance, to solve the relevant inverse problem based on observations of the system(data), or, in statistical terminology, to make inference on underlying parametersand model components that characterize the mechanisms from the data. In manysettings, there is a realization that dynamical systems should incorporate stochas-tic components to take account of heterogeneity in underlying mechanisms, e.g.,inter-cell variation in viral production delays in within-host HIV dynamics. In addi-tion, heterogeneity may arise from data structure in which observations are collectedfrom several individuals or samples with the broader focus on understanding not justindividual-level dynamics but variation in mechanistic behavior across the popula-tion. In both cases, it is natural to treat unknown, unobservable system parametersas random quantities whose distribution is to be estimated. There is a large inverseproblem literature for systems without such stochastic components; even here, for-ward solutions (i.e., solutions of the dynamics when parameters are specified) forcomplex systems often necessitate sophisticated techniques, so that inverse prob-lem methodologies pose considerable challenges. Similarly, there is a vast statisticalliterature devoted to estimation and accounting for uncertainty in highly nonlinearmodels with random components, involving hierarchical specifications and complexcomputational issues.

With the potential overlap and emerging challenges, there has been interactionbetween applied mathematicians and statisticians to develop relevant inverse prob-lem/statistical inferential methodologies. When combined, the computational andtheoretical hurdles posed by both mathematical and statistical issues are substantial,and their resolution requires an integrated effort. The research from Inverse Prob-

1.2 The Frontiers of Research at SAMSI 5

lem Methodology in Complex Stochastic Models entailed facilitating the essentialcooperative effort required to catalyze collaborative research in this direction.

1.2.1.3 Large-scale Computer Models for Environmental Systems, 2002–2003

Modeling of complex environmental systems is a major area of involvement ofstatisticians and applied mathematicians with disciplinary scientists. Yet it is alsoa prime example of the differing emphases of the two groups, applied mathemati-cians focusing on deterministic modeling of the systems and statisticians on utilizingthe (often extensive) data for development and analysis of more generic stochasticmodels. There are two major areas of particular interest and scientific importance.

Large-scale atmospheric models. Much contemporary work in atmospheric sci-ence revolves around large-scale models such as NCAR’s Community Climate Sys-tem Model (which includes atmosphere, ocean, land, and ice), mesoscale modelssuch as the Penn-State/NCAR MM5 model, and the multi-scale air quality model(Models-3) developed by the EPA. Such models are generally deterministic, buttheir formulation and use involve a variety of sources of uncertainty, such as un-known initial and boundary conditions; “model parameterizations” (the treatmentof relevant physical phenomena varying at scales smaller than the grid size of themodel, e.g., clouds); and numerical stability issues. Some climatologists have begunwork on “stochastic parameterizations.” Other basic issues central to these modelsinclude the need for an improved scientific understanding of unresolvable, subgrid-scale phenomena, and large-scale (chaotic) non-determinism.

Flows in porous media. Porous medium dynamics is an active and increasingly in-terdisciplinary research area with applications from a diverse set of fields includingapplied sciences (such as environmental studies, geology, hydrology, petroleum en-gineering, civil engineering, and soil physics), and basic sciences (such as physics,chemistry, and mathematics). However, there were few collaborative efforts thathave equal footing in mathematics, disciplinary science, and statistics. The SAMSIprogram was built around four major themes: model formulation, parameter estima-tion, numerical methods, and design and optimization.

1.2.1.4 Data Mining and Machine Learning (DMML), 2003–2004

Data mining and machine learning — the discovery of patterns, information, andknowledge in what are almost always large, complex (and, often, unstructured) datasets — have seen a proliferation of techniques over the past decade. Yet, there re-mains incomplete understanding of fundamental statistical and computational issuesin data mining, machine learning and large (sample size or dimension) data sets.

The goals of the DMML program were to advance significantly the understand-ing of fundamental statistical and computational issues in data mining, machinelearning, and large data sets, to articulate future research needs for DMML, espe-

6 1 Introduction

cially from the perspective of the statistical sciences, and to catalyze the formationof collaborations among statistical, mathematical, and computer scientists to pursuethe research agenda.

By almost every measure, the program was a strong success. The high pointsare (i) a deeper understanding of the points of connection between data mining andstatistical theory and methodology; (ii) effective analyses of a large, extremely com-plex testbed database provided by General Motors (GM), an affiliate of NISS andSAMSI, thus also strengthening SAMSI’s industrial connections; (iii) a strong andcontinuing collaboration in the area of metabolomics, involving chemists, computerscientists, and statistical scientists; and (iv) a range of specific progress on issuesranging from false discovery rates to overcompleteness to support vector machines.

1.2.1.5 Network Modeling for the Internet, 2003–2004

Because of the size and complexity of the internet, and the nature of the protocols,internet traffic has proved to be very challenging to model effectively. Yet modelingis critical to improving quality of service and efficiency. The main research goalof this program was to address these issues by bringing together researchers fromthree communities: (a) applied probabilists studying heavy traffic queueing theoryand fluid flow models; (b) mainstream internet traffic measurers/modelers and hard-ware/software architects; and (c) statisticians.

The timing was right for simultaneous interaction among all three communities,because of the trend away from dealing with quality of service issues through over-provisioning of equipment. This trend suggested that heavy traffic models wouldbe ideally situated to play a leading role in future modeling of internet traffic, andin attaining deeper understanding of the complex drivers behind quality of service.The following topics were of particular interest.

Changepoints and extremes: To explore approaches in which the transitions be-tween bursty and non-bursty internet traffic are considered changepoints, with mod-els and methods from extreme value theory used to characterize the bursty periods.

Formulation of suite of models: To develop useful statistical models for internettraffic flow that are simple to analyze and simulate, and can capture the character-istics of actual traffic data that are important to electronics engineers and computerscientists.

Multifractional Brownian and stable motion: To capture two major characteristicfeatures of the network traffic: time scale invariance (statistical self-similarity) andlong-range dependence.

Structural breaks: To explore structural breaks in the context of internet trafficmodeling where evidence of long-range dependence is also ubiquitous.

1.2 The Frontiers of Research at SAMSI 7

1.2.1.6 Multiscale Model Development and Control Design, 2003–2004

Multiscale analysis is ubiquitous in the modeling, design, and control of high per-formance systems utilizing novel material architectures. In applications includingquantum computing, nanopositioning, granular flows, artificial muscle design, flowcontrol, liquid crystal polymers, and actuator implants to stimulate tissue and bonegrowth, it is necessary to develop multiscale modeling hierarchies ranging fromquantum to system levels for time scales ranging from nanoseconds to hours. Con-trol techniques must be designed in concert with the models to guarantee the sym-biosis required to achieve the novel design specifications. A crucial component ofmultiscale analysis is the development of homogenization techniques to bridge dis-parate temporal and spatial scales. This is necessitated by the fact that even withprojected computing capabilities, monoscale models are prohibitively large to per-mit feasible system design or control implementation.

A number of these issues can be illustrated in the context of two prototypicalmaterials, piezoceramics and ionic polymers, which are being considered for appli-cations ranging from quantum storage to artificial muscle design. In both cases, theunique transducer properties provided by the compounds are inherently coupled tohighly nonlinear dynamics which must be accommodated in material characteriza-tion, numerical approximation, device design, and control implementation.

The real-time approximation of comprehensive material models for device de-sign and model-based control implementation is a significant challenge which mustbe addressed before novel material constructs and device architectures can achievetheir full potential. The realization of these goals requires the development ofreduced-order models which retain fundamental physics but are sufficiently low-order to permit real-time implementation.

Other components include control design, a crucial aspect of which is robustnesswith regard to disturbance and unmodeled dynamics. Deterministic robust controldesigns often provide uncertainty bounds which are overly conservative and henceprovide limited control authority. Alternatively, one can provide statistical boundson uncertainties.

1.2.1.7 Computational Biology of Infectious Diseases, 2004–2005

Infectious disease remains a major cause of suffering and mortality among peoplein the developing world, and a constant threat worldwide. The advent of genomescience and the continuing rapid growth of computational resources together her-alded an opportunity for the mathematical and statistical sciences to play a keyrole in the elucidation of pathogenesis and immunity and in the development of thenext generation of therapies and global strategies. The program encompassed bothgenomic and population-level studies, including microbial and immunological ge-nomics, vaccine design and proteomics, drug target identification, gene expressionmodeling and analysis, molecular evolution of host-microbe systems, drug resis-

8 1 Introduction

tance, epidemiology and public health, systems immunology, and microbial ecol-ogy.

1.2.1.8 Latent Variable Models in the Social Sciences, 2004–2005

Latent variables are widespread in the social sciences. Whether it is intelligence orsocioeconomic status, many variables cannot be directly measured. Factor analy-sis, latent class analysis, structural equation models, error-in-variable models, anditem response theory illustrate models that incorporate latent variables. Issues ofcausality, multilevel models, longitudinal data, measurement error and categoricalvariables in latent variable models were examined.

Categorical variables. Many categorical observed variables in the social sciencesare imperfect measures of underlying latent variables. Statistical issues emergewhen categorical observed variables are part of a model with latent variables or withmeasurement error. There were mainly two approaches to models with categoricaloutcomes: James Hardin’s recent advances in models that correct for measurementerror in nonlinear models within the GLM framework, and Ken Bollen’s two-stageleast squares approach to latent variable models.

Complex surveys. A range of issues arise from survey data. Among these, twoissues were of particular interest: (i) latent class analysis (LCA) of measurementerror in surveys; and (ii) weighting and estimation for complex sample designs.

1.2.1.9 Data Assimilation for Geophysical Systems, 2004–2005

Data assimilation aims at accurate re-analysis, estimation and prediction of an un-known, true state by merging observed information into a model. This issue arisesin all scientific areas that enjoy a profusion of data.

The problem of assimilating data into a geophysical system, such as the onerelated to the atmosphere or oceans, is both fundamental in that it aims at the esti-mation and prediction of an unknown true state, and challenging as it does not nat-urally afford a clean solution. It has two equally important elements: observationsand computational models. Observations measured by instruments provide directinformation of the true state. Such observations are heterogeneous, inhomogeneousin space, irregular in time, and subject to differing accuracies. In contrast, computa-tional models use knowledge of the underlying physics and dynamics to provide adescription of state evolution in time. Models are also far from perfect: due to modelerror, uncertainty in the initial conditions and computational limitations, model evo-lution cannot accurately generate the true state.

In its broadest sense, data assimilation (henceforth referred to as DA) arises inall scientific areas that enjoy a profusion of data. By its very nature, DA is a com-plex interdisciplinary subject that involves statistics, applied mathematics, and therelevant domain science. Driven by operational demands for numerical weather pre-

1.2 The Frontiers of Research at SAMSI 9

diction, however, the development of DA so far has been predominantly led by thegeophysical community. In order to further DA beyond the current state-of-art, thedevelopment of effective methods must now be viewed as one of the fundamentalchallenges in scientific prediction.

1.2.1.10 Financial Mathematics, Statistics and Econometrics, 2005–2006

The goal of the study on Financial Mathematics, Statistics and Econometrics (FMSE)was to identify short and long term research directions deemed necessary to achieveboth fundamental and practical advances in this rapidly growing field and to ini-tiate collaborative research programs — among mathematicians, statisticians, andeconomists — focused on the multi-disciplinary and overlapping set of fields whichinvolves disciplines such as: Applied Mathematics, Economics and Finance, Econo-metrics, and Statistics. A prominent theme throughout both the workshop and pro-gram was the necessity of exploiting the natural synergy between areas of financialmathematics, statistics, and econometrics. The goal of the SAMSI program in Fi-nancial Mathematics and Econometrics was to bring together these disciplines andinitiate a discussion regarding what is really important and what is missing in threeessential tasks.

Modeling. Model development was considered in domains ranging from financialand energy derivatives to real options.

Data. The size of financial data can be considerable when looking at high frequencydata for large numbers of stocks for example.

Computation. Once a model has been written and calibrated to data, it remains nec-essary to compute quantities of interest. These three key themes transpired throughthe entire program and all its activities, including workshops, courses, and the di-versity of visitors and participants.

1.2.1.11 National Defense and Homeland Security, 2005–2006

For several years, groups of researchers have been seeking to define appropriateroles for the statistical sciences, applied mathematical sciences, and decision sci-ences in problems of National Defense and Homeland Security (NDHS). Many ef-forts have focused on short-term applicability of existing methods and tools, ratherthan articulating or initiating a longer-term research agenda. Moreover, none of themhas really spanned the statistical sciences, the applied mathematical sciences, andthe decision sciences. Perhaps most important point is that, despite progress, theseefforts have not “jelled” to produce a self-sustaining research momentum in the sta-tistical sciences, applied mathematical sciences, and decision sciences on problemsof NDHS. The NDHS program was meant fill this gap, in part by providing proofof concept that the necessary collaborations are feasible.