Bayesian Methods for Data Analysis, Third Edition

by Carlin; Bradley P.

• ISBN13: 9781584886976
• ISBN10: 1584886978
• Edition: 3rd
• Format: Hardcover
• Copyright: 2008-06-30
• Publisher: Chapman & Hall/

Summary

The third edition of Bayesian Methods for Data Analysis has been updated to provide a more accessible introduction to the foundations of Bayesian analysis along with a stronger focus on applications, including case studies in biostatistics, epidemiology, and genetics. This edition features a new chapter on Bayesian design that presents Bayesian clinical trials and special topics such as missing data and causality. With an emphasis on computation, there is also expanded coverage of WinBUGS, R, and BRugs. The book contains additional exercises and solutions for undergraduate students, graduate students, and researchers in statistics and biostatistics.

Table of Contents

Preface to the Third Edition	p. xiii
Approaches for statistical inference	p. 1
Introduction	p. 1
Motivating vignettes	p. 2
Personal probability	p. 2
Missing data	p. 2
Bioassay	p. 3
Attenuation adjustment	p. 4
Defining the approaches	p. 4
The Bayes-frequentist controversy	p. 6
Some basic Bayesian models	p. 10
A Gaussian/Gaussian (normal/normal) model	p. 11
A beta/binomial model	p. 11
Exercises	p. 13
The Bayes approach	p. 15
Introduction	p. 15
Prior distributions	p. 27
Elicited priors	p. 28
Conjugate priors	p. 32
Noninformative priors	p. 36
Other prior construction methods	p. 40
Bayesian inference	p. 41
Point estimation	p. 41
Interval estimation	p. 48
Hypothesis testing and Bayes factors	p. 50
Hierarchical modeling	p. 59
Normal linear models	p. 59
Effective model size and the DIC criterion	p. 70
Model assessment	p. 79
Diagnostic measures	p. 79
Model averaging	p. 89
Nonparametric methods	p. 93
Exercises	p. 98
Bayesian computation	p. 105
Introduction	p. 105
Asymptotic methods	p. 108
Normal approximation	p. 108
Laplace's method	p. 110
Noniterative Monte Carlo methods	p. 112
Direct sampling	p. 112
Indirect methods	p. 115
Markov chain Monte Carlo methods	p. 120
Gibbs sampler	p. 121
Metropolis-Hastings algorithm	p. 130
Slice sampler	p. 139
Hybrid forms, adaptive MCMC, and other algorithms	p. 140
Variance estimation	p. 150
Convergence monitoring and diagnosis	p. 152
Exercises	p. 159
Model criticism and selection	p. 167
Bayesian modeling	p. 168
Linear models	p. 168
Nonlinear models	p. 174
Binary data models	p. 176
Bayesian robustness	p. 181
Sensitivity analysis	p. 181
Prior partitioning	p. 188
Model assessment	p. 194
Bayes factors via marginal density estimation	p. 196
Direct methods	p. 197
Using Gibbs sampler output	p. 198
Using Metropolis-Hastings output	p. 200
Bayes factors via sampling over the model space	p. 201
Product space search	p. 203
"Metropolized" product space search	p. 205
Reversible jump MCMC	p. 206
Using partial analytic structure	p. 208
Other model selection methods	p. 210
Penalized likelihood criteria: AIC, BIC, and DIC	p. 210
Predictive model selection	p. 215
Exercises	p. 217
The empirical Bayes approach	p. 225
Introduction	p. 225
Parametric EB (PEB) point estimation	p. 226
Gaussian/Gaussian models	p. 227
Computation via the EM algorithm	p. 228
EB performance of the PEB	p. 234
Stein estimation	p. 236
Nonparametric EB (NPEB) point estimation	p. 240
Compound sampling models	p. 240
Simple NPEB (Robbins' method)	p. 240
Interval estimation	p. 244
Morris' approach	p. 245
Marginal posterior approach	p. 246
Bias correction approach	p. 248
Bayesian processing and performance	p. 251
Univariate stretching with a two-point prior	p. 251
Multivariate Gaussian model	p. 252
Frequentist performance	p. 253
Gaussian/Gaussian model	p. 254
Beta/binomial model	p. 255
Empirical Bayes performance	p. 258
Point estimation	p. 259
Interval estimation	p. 262
Exercises	p. 265
Bayesian design	p. 269
Principles of design	p. 269
Bayesian design for frequentist analysis	p. 269
Bayesian design for Bayesian analysis	p. 271
Bayesian clinical trial design	p. 274
Classical versus Bayesian trial design	p. 275
Bayesian assurance	p. 277
Bayesian indifference zone methods	p. 279
Other Bayesian approaches	p. 282
Extensions	p. 286
Applications in drug and medical device trials	p. 287
Binary endpoint drug trial	p. 287
Cox regression device trial with interim analysis	p. 297
Exercises	p. 308
Special methods and models	p. 311
Estimating histograms and ranks	p. 311
Bayesian ranking	p. 311
Histogram and triple goal estimates	p. 324
Robust prior distributions	p. 328
Order restricted inference	p. 333
Longitudinal data models	p. 334
Continuous and categorical time series	p. 341
Survival analysis and frailty models	p. 343
Statistical models	p. 343
Treatment effect prior determination	p. 344
Computation and advanced models	p. 345
Sequential analysis	p. 346
Model and loss structure	p. 347
Backward induction	p. 348
Forward sampling	p. 349
Spatial and spatio-temporal models	p. 352
Point source data models	p. 353
Regional summary data models	p. 356
Exercises	p. 361
Case studies	p. 373
Analysis of longitudinal AIDS data	p. 374
Introduction and background	p. 374
Modeling of longitudinal CD4 counts	p. 375
CD4 response to treatment at two months	p. 384
Survival analysis	p. 385
Discussion	p. 386
Robust analysis of clinical trials	p. 387
Clinical background	p. 387
Interim monitoring	p. 388
Prior robustness and prior scoping	p. 393
Sequential decision analysis	p. 398
Discussion	p. 401
Modeling of infectious diseases	p. 402
Introduction and data	p. 402
Stochastic compartmental model	p. 403
Parameter estimation and model building	p. 406
Results	p. 409
Discussion	p. 414
Appendices	p. 417
Distributional catalog	p. 419
Discrete	p. 420
Univariate	p. 420
Multivariate	p. 421
Continuous	p. 421
Univariate	p. 421
Multivariate	p. 425
Decision theory	p. 429
Introduction	p. 429
Risk and admissibility	p. 430
Unbiased rules	p. 431
Bayes rules	p. 433
Minimax rules	p. 434
Procedure evaluation and other unifying concepts	p. 435
Mean squared error (MSE)	p. 435
The variance-bias tradeoff	p. 435
Other loss functions	p. 436
Generalized absolute loss	p. 437
Testing with a distance penalty	p. 437
A threshold loss function	p. 437
Multiplicity	p. 438
Multiple testing	p. 439
Additive loss	p. 439
Non-additive loss	p. 440
Exercises	p. 441
Answers to selected exercises	p. 445
References	p. 487
Author index	p. 521
Subject index	p. 529
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