Table of contents
Preface v
Contributors xvii
Ch. 1. Bayesian Inference for Causal Effects 1
Donald B. Rubin
1. Causal inference primitives 1
2. A brief history of the potential outcomes framework 5
3. Models for the underlying data – Bayesian inference 7
4. Complications 12
References 14
Ch. 2. Reference Analysis 17
José M. Bernardo
1. Introduction and notation 17
2. Intrinsic discrepancy and expected information 22
3. Reference distributions 29
4. Reference inference summaries 61
5. Related work 71
Acknowledgements 73
References 73
Further reading 82
Ch. 3. Probability Matching Priors 91
Gauri Sankar Datta and Trevor J. Sweeting
1. Introduction 91
2. Rationale 93
3. Exact probability matching priors 94
4. Parametric matching priors in the one-parameter case 95
5. Parametric matching priors in the multiparameter case 97
6. Predictive matching priors 107
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viii Table of contents
7. Invariance of matching priors 110
8. Concluding remarks 110
Acknowledgements 111
References 111
Ch. 4. Model Selection and Hypothesis Testing based on Objective Probabilities
and Bayes Factors 115
Luis Raúl Pericchi
1. Introduction 115
2. Objective Bayesian model selection methods 121
3. More general training samples 143
4. Prior probabilities 145
5. Conclusions 145
Acknowledgements 146
References 146
Ch. 5. Role of P-values and other Measures of Evidence in Bayesian Analysis 151
Jayanta Ghosh, Sumitra Purkayastha and Tapas Samanta
1. Introduction 151
2. Conflict between P-values and lower bounds to Bayes factors and posterior probabilities: Case of a
sharp null 153
3. Calibration of P-values 158
4. Jeffreys–Lindley paradox 159
5. Role of the choice of an asymptotic framework 159
6. One-sided null hypothesis 163
7. Bayesian P-values 165
8. Concluding remarks 168
References 169
Ch. 6. Bayesian Model Checking and Model Diagnostics 171
Hal S. Stern and Sandip Sinharay
1. Introduction 171
2. Model checking overview 172
3. Approaches for checking if the model is consistent with the data 173
4. Posterior predictive model checking techniques 176
5. Application 1 180
6. Application 2 182
7. Conclusions 190
References 191
Table of contents ix
Ch. 7. The Elimination of Nuisance Parameters 193
Brunero Liseo
1. Introduction 193
2. Bayesian elimination of nuisance parameters 196
3. Objective Bayes analysis 199
4. Comparison with other approaches 204
5. The Neyman and Scott class of problems 207
6. Semiparametric problems 213
7. Related issues 215
Acknowledgements 217
References 217
Ch. 8. Bayesian Estimation of Multivariate Location Parameters 221
Ann Cohen Brandwein and William E. Strawderman
1. Introduction 221
2. Bayes, admissible and minimax estimation 222
3. Stein estimation and the James–Stein estimator 225
4. Bayes estimation and the James–Stein estimator for the mean of the multivariate normal distribution
with identity covariance matrix 230
5. Generalizations for Bayes and the James–Stein estimation or the mean for the multivariate normal
distribution with known covariance matrix Σ 235
6. Conclusion and extensions 242
References 243
Ch. 9. Bayesian Nonparametric Modeling and Data Analysis: An Introduction 245
Timothy E. Hanson, Adam J. Branscum and Wesley O. Johnson
1. Introduction to Bayesian nonparametrics 245
2. Probability measures on spaces of probability measures 247
3. Illustrations 258
4. Concluding remarks 273
References 274
Ch. 10. Some Bayesian Nonparametric Models 279
Paul Damien
1. Introduction 279
2. Random distribution functions 281
3. Mixtures of Dirichlet processes 284
4. Random variate generation for NTR processes 287
5. Sub-classes of random distribution functions 293
6. Hazard rate processes 299
7. Polya trees 303
8. Beyond NTR processes and Polya trees 307
References 308
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Ch. 11. Bayesian Modeling in the Wavelet Domain 315
Fabrizio Ruggeri and Brani Vidakovic
1. Introduction 315
2. Bayes and wavelets 317
3. Other problems 333
Acknowledgements 335
References 335
Ch. 12. Bayesian Nonparametric Inference 339
Stephen Walker
1. Introduction 339
2. The Dirichlet process 342
3. Neutral to the right processes 348
4. Other priors 353
5. Consistency 359
6. Nonparametric regression 364
7. Reinforcement and exchangeability 365
8. Discussion 367
Acknowledgement 367
References 368
Ch. 13. Bayesian Methods for Function Estimation 373
Nidhan Choudhuri, Subhashis Ghosal and Anindya Roy
1. Introduction 373
2. Priors on infinite-dimensional spaces 374
3. Consistency and rates of convergence 384
4. Estimation of cumulative probability distribution 394
5. Density estimation 396
6. Regression function estimation 402
7. Spectral density estimation 404
8. Estimation of transition density 406
9. Concluding remarks 408
References 409
Ch. 14. MCMC Methods to Estimate Bayesian Parametric Models 415
Antonietta Mira
1. Motivation 415
2. Bayesian ingredients 416
3. Bayesian recipe 416
4. How can the Bayesian pie burn 417
5. MCMC methods 418
6. The perfect Bayesian pie: How to avoid “burn-in” issues 431
7. Conclusions 432
References 433
Table of contents xi
Ch. 15. Bayesian Computation: From Posterior Densities to Bayes Factors, Marginal
Likelihoods, and Posterior Model Probabilities 437
Ming-Hui Chen
1. Introduction 437
2. Posterior density estimation 438
3. Marginal posterior densities for generalized linear models 447
4. Savage–Dickey density ratio 449
5. Computing marginal likelihoods 450
6. Computing posterior model probabilities via informative priors 451
7. Concluding remarks 456
References 456
Ch. 16. Bayesian Modelling and Inference on Mixtures of Distributions 459
Jean-Michel Marin, Kerrie Mengersen and Christian P. Robert
1. Introduction 459
2. The finite mixture framework 460
3. The mixture conundrum 466
4. Inference for mixtures models with known number of components 480
5. Inference for mixture models with unknown number of components 496
6. Extensions to the mixture framework 501
Acknowledgements 503
References 503
Ch. 17. Simulation Based Optimal Design 509
Peter Müller
1. Introduction 509
2. Monte Carlo evaluation of expected utility 511
3. Augmented probability simulation 511
4. Sequential design 513
5. Multiple comparisons 514
6. Calibrating decision rules by frequentist operating characteristics 515
7. Discussion 516
References 517
Ch. 18. Variable Selection and Covariance Selection in Multivariate Regression
Models 519
Edward Cripps, Chris Carter and Robert Kohn
1. Introduction 519
2. Model description 521
3. Sampling scheme 526
4. Real data 527
5. Simulation study 541
6. Summary 550
References 551
xii Table of contents
Ch. 19. Dynamic Models 553
Helio S. Migon, Dani Gamerman, Hedibert F. Lopes and
Marco A.R. Ferreira
1. Model structure, inference and practical aspects 553
2. Markov Chain Monte Carlo 564
3. Sequential Monte Carlo 573
4. Extensions 580
Acknowledgements 584
References 584
Ch. 20. Bayesian Thinking in Spatial Statistics 589
Lance A. Waller
1. Why spatial statistics? 589
2. Features of spatial data and building blocks for inference 590
3. Small area estimation and parameter estimation in regional data 592
4. Geostatistical prediction 599
5. Bayesian thinking in spatial point processes 608
6. Recent developments and future directions 617
References 618
Ch. 21. Robust Bayesian Analysis 623
Fabrizio Ruggeri, David Ríos Insua and Jacinto Martín
1. Introduction 623
2. Basic concepts 625
3. A unified approach 639
4. Robust Bayesian computations 647
5. Robust Bayesian analysis and other statistical approaches 657
6. Conclusions 661
Acknowledgements 663
References 663
Ch. 22. Elliptical Measurement Error Models – A Bayesian Approach 669
Heleno Bolfarine and R.B. Arellano-Valle
1. Introduction 669
2. Elliptical measurement error models 671
3. Diffuse prior distribution for the incidental parameters 673
4. Dependent elliptical MEM 675
5. Independent elliptical MEM 680
6. Application 686
Acknowledgements 687
References 687
Table of contents xiii
Ch. 23. Bayesian Sensitivity Analysis in Skew-elliptical Models 689
I. Vidal, P. Iglesias and M.D. Branco
1. Introduction 689
2. Definitions and properties of skew-elliptical distributions 692
3. Testing of asymmetry in linear regression model 699
4. Simulation results 705
5. Conclusions 706
Acknowledgements 707
Appendix A: Proof of Proposition 3.7 707
References 710
Ch. 24. Bayesian Methods for DNA Microarray Data Analysis 713
Veerabhadran Baladandayuthapani, Shubhankar Ray and
Bani K. Mallick
1. Introduction 713
2. Review of microarray technology 714
3. Statistical analysis of microarray data 716
4. Bayesian models for gene selection 717
5. Differential gene expression analysis 730
6. Bayesian clustering methods 735
7. Regression for grossly overparametrized models 738
8. Concluding remarks 739
Acknowledgements 739
References 739
Ch. 25. Bayesian Biostatistics 743
David B. Dunson
1. Introduction 743
2. Correlated and longitudinal data 745
3. Time to event data 748
4. Nonlinear modeling 752
5. Model averaging 755
6. Bioinformatics 756
7. Discussion 757
References 758
Ch. 26. Innovative Bayesian Methods for Biostatistics and Epidemiology 763
Paul Gustafson, Shahadut Hossain and Lawrence McCandless
1. Introduction 763
2. Meta-analysis and multicentre studies 765
xiv Table of contents
3. Spatial analysis for environmental epidemiology 768
4. Adjusting for mismeasured variables 769
5. Adjusting for missing data 773
6. Sensitivity analysis for unobserved confounding 775
7. Ecological inference 777
8. Bayesian model averaging 779
9. Survival analysis 782
10. Case-control analysis 784
11. Bayesian applications in health economics 786
12. Discussion 787
References 789
Ch. 27. Bayesian Analysis of Case-Control Studies 793
Bhramar Mukherjee, Samiran Sinha and Malay Ghosh
1. Introduction: The frequentist development 793
2. Early Bayesian work on a single binary exposure 796
3. Models with continuous and categorical exposure 798
4. Analysis of matched case-control studies 803
5. Some equivalence results in case-control studies 813
6. Conclusion 815
References 816
Ch. 28. Bayesian Analysis of ROC Data 821
Valen E. Johnson and Timothy D. Johnson
1. Introduction 821
2. A Bayesian hierarchical model 826
3. An example 832
References 833
Ch. 29. Modeling and Analysis for Categorical Response Data 835
Siddhartha Chib
1. Introduction 835
2. Binary responses 840
3. Ordinal response data 846
4. Sequential ordinal model 848
5. Multivariate responses 850
6. Longitudinal binary responses 858
7. Longitudinal multivariate responses 862
8. Conclusion 865
References 865
Table of contents xv
Ch. 30. Bayesian Methods and Simulation-Based Computation for Contingency
Tables 869
James H. Albert
1. Motivation for Bayesian methods 869
2. Advances in simulation-based Bayesian calculation 869
3. Early Bayesian analyses of categorical data 870
4. Bayesian smoothing of contingency tables 872
5. Bayesian interaction analysis 876
6. Bayesian tests of equiprobability and independence 879
7. Bayes factors for GLM’s with application to log-linear models 881
8. Use of BIC in sociological applications 884
9. Bayesian model search for loglinear models 885
10. The future 888
References 888
Ch. 31. Multiple Events Time Data: A Bayesian Recourse 891
Debajyoti Sinha and Sujit K. Ghosh
1. Introduction 891
2. Practical examples 892
3. Semiparametric models based on intensity functions 894
4. Frequentist methods for analyzing multiple event data 897
5. Prior processes in semiparametric model 899
6. Bayesian solution 901
7. Analysis of the data-example 902
8. Discussions and future research 904
References 905
Ch. 32. Bayesian Survival Analysis for Discrete Data with Left-Truncation and
Interval Censoring 907
Chong Z. He and Dongchu Sun
1. Introduction 907
2. Likelihood functions 910
3. Bayesian analysis 913
4. Posterior distributions and Bayesian computation 919
5. Applications 921
6. Comments 927
Acknowledgements 927
References 927
xvi Table of contents
Ch. 33. Software Reliability 929
Lynn Kuo
1. Introduction 929
2. Dynamic models 930
3. Bayesian inference 935
4. Model selection 956
5. Optimal release policy 958
6. Remarks 959
References 959
Ch. 34. Bayesian Aspects of Small Area Estimation 965
Tapabrata Maiti
1. Introduction 965
2. Some areas of application 965
3. Small area models 966
4. Inference from small area models 968
5. Conclusion 980
Acknowledgements 981
References 981
Ch. 35. Teaching Bayesian Thought to Nonstatisticians 983
Dalene K. Stangl
1. Introduction 983
2. A brief literature review 984
3. Commonalities across groups in teaching Bayesian methods 984
4. Motivation and conceptual explanations: One solution 986
5. Conceptual mapping 988
6. Active learning and repetition 988
7. Assessment 990
8. Conclusions 991
References 991
Colour figures 993
Subject Index 1005
Contents of Previous Volumes 1017