Bayes and empirical Bayes methods for data analysis /
Bradley P. Carlin and Thomas A. Louis.
1st ed.
London ; New York : Chapman & Hall, c1996.
xvi, 399 p. : ill. ; 23 cm.
0412056119, 9780412056116
More Details
London ; New York : Chapman & Hall, c1996.
catalogue key
Includes bibliographical references (p.[363]-386) and indexes.
A Look Inside
About the Author
Author Affiliation
Bradley P. Carlin is a Professor in the Division of Biostatistics in the School of Public Health at the University of Minnesota, MN Thomas A. Louis is a Senior Statistician at The RAND Corporation in Santa Monica, CA
Main Description
Recent advances in computing-leading to the ability to evaluate increasingly complex models-has resulted in a growing popularity of Bayes and empirical Bayes (EB) methods in statistical practice. Bayes and Empirical Bayes Methods for Data Analysis answers the need for a ready reference that can be read and appreciated by practicing statisticians as well as graduate students. It introduces Bayes and EB methods, demonstrates their usefulness in challenging applied settings, and shows how they can be implemented using modern Markov chain Monte Carlo (MCMC) computational methods. Avoiding philosophical nit-picking, it shows how properly structured Bayes and EB procedures have good frequentist and Bayesian performance both in theory and practice. The authors have chosen a very practical focus for their work, offering real solution methods to researchers with challenging problems. Beginning with an outline of the decision-theoretic tools needed to compare procedures, the book presents the basics of Bayes and EB approaches. The authors evaluate the frequentist and empirical Bayes performance of these approaches in a variety of settings and identify both virtues and drawbacks. The second half of the book stresses applications. If offers an extensive discussion of modern Bayesian computation methods-including the Gibbs sampler and the Metropolis-Hastings algorithm. It describes data analytic tasks, and offers guidelines on using a variety of special methods and models. The authors conclude with three fully worked case studies of real data sets.
Unpaid Annotation
This book shows how Bayes and empirical Bayes methods operate in theory and practice and substantially benefit applied statisticians and graduate students.
Table of Contents
Preface to the Second Editionp. xiii
Preface to the First Editionp. xv
Approaches for statistical inferencep. 1
Introductionp. 1
Motivating vignettesp. 2
Personal probabilityp. 2
Missing datap. 2
Bioassayp. 3
Attenuation adjustmentp. 4
Defining the approachesp. 4
The Bayes-frequentist controversyp. 6
Some basic Bayesian modelsp. 10
A Gaussian/Gaussian (normal/normal) modelp. 11
A beta/binomial modelp. 11
Exercisesp. 13
The Bayes approachp. 17
Introductionp. 17
Prior distributionsp. 22
Elicited priorsp. 23
Conjugate priorsp. 25
Noninformative priorsp. 28
Other prior construction methodsp. 31
Bayesian inferencep. 32
Point estimationp. 32
Interval estimationp. 35
Hypothesis testing and Bayes factorsp. 38
Example: Consumer preference datap. 42
Model assessmentp. 46
Diagnostic measuresp. 46
Model averagingp. 49
Nonparametric methodsp. 51
Exercisesp. 53
The empirical Bayes approachp. 57
Introductionp. 57
Nonparametric EB (NPEB) point estimationp. 58
Compound sampling modelsp. 58
Simple NPEB (Robbins' method)p. 59
Example: Accident datap. 60
Parametric EB (PEB) point estimationp. 62
Gaussian/Gaussian modelsp. 62
Beta/binomial modelp. 67
EB performance of the PEBp. 69
Stein estimationp. 70
Computation via the EM algorithmp. 74
EM for PEBp. 74
Computing the observed informationp. 76
EM for NPEBp. 77
Speeding convergence and generalizationsp. 77
Interval estimationp. 78
Morris' approachp. 79
Marginal posterior approachp. 80
Bias correction approachp. 82
Generalization to regression structuresp. 85
Exercisesp. 86
Performance of Bayes proceduresp. 89
Bayesian processingp. 90
Univariate stretching with a two-point priorp. 90
Multivariate Gaussian modelp. 90
Frequentist performance: Point estimatesp. 92
Gaussian/Gaussian modelp. 92
Beta/binomial modelp. 94
Generalizationp. 97
Frequentist performance: Confidence intervalsp. 98
Beta/binomial modelp. 98
Fieller-Creasy problemp. 103
Empirical Bayes performancep. 108
Point estimationp. 108
Interval estimationp. 111
Design of experimentsp. 114
Bayesian design for frequentist analysisp. 114
Bayesian design for Bayesian analysisp. 116
Exercisesp. 119
Bayesian computationp. 121
Introductionp. 121
Asymptotic methodsp. 122
Normal approximationp. 122
Laplace's methodp. 124
Noniterative Monte Carlo methodsp. 129
Direct samplingp. 129
Indirect methodsp. 131
Markov chain Monte Carlo methodsp. 137
Substitution sampling and data augmentationp. 137
Gibbs samplingp. 141
Metropolis-Hastings algorithmp. 152
Hybrid forms and other algorithmsp. 159
Variance estimationp. 170
Convergence monitoring and diagnosisp. 172
Exercisesp. 183
Model criticism and selectionp. 193
Bayesian robustnessp. 194
Sensitivity analysisp. 194
Prior partitioningp. 199
Model assessmentp. 204
Bayes factors via marginal density estimationp. 206
Direct methodsp. 207
Using Gibbs sampler outputp. 208
Using Metropolis-Hastings outputp. 210
Bayes factors via sampling over the model spacep. 211
Product space searchp. 213
"Metropolized" product space searchp. 215
Reversible jump MCMCp. 216
Using partial analytic structurep. 217
Other model selection methodsp. 219
Penalized likelihood criteriap. 220
Predictive model selectionp. 223
Exercisesp. 225
Special methods and modelsp. 229
Estimating histograms and ranksp. 229
Model and inferential goalsp. 230
Triple goal estimatesp. 232
Smoothing and robustnessp. 234
Order restricted inferencep. 237
Nonlinear modelsp. 239
Longitudinal data modelsp. 242
Continuous and categorical time seriesp. 244
Survival analysis and frailty modelsp. 246
Statistical modelsp. 246
Treatment effect prior determinationp. 247
Computation and advanced modelsp. 248
Sequential analysisp. 249
Model and loss structurep. 250
Backward inductionp. 252
Forward samplingp. 252
Spatial and spatio-temporal modelsp. 255
Point source data modelsp. 256
Regional summary data modelsp. 259
Exercisesp. 264
Case studiesp. 275
Analysis of longitudinal AIDS datap. 276
Introduction and backgroundp. 276
Modeling of longitudinal CD4 countsp. 277
CD4 response to treatment at two monthsp. 286
Survival analysisp. 287
Discussionp. 289
Robust analysis of clinical trialsp. 290
Clinical backgroundp. 290
Interim monitoringp. 290
Prior robustness and prior scopingp. 295
Sequential decision analysisp. 301
Discussionp. 304
Spatio-temporal mapping of lung cancer ratesp. 305
Introductionp. 305
Data and model descriptionp. 307
Computational considerationsp. 309
Model fitting, validation, and comparisonp. 309
Discussionp. 315
Appendicesp. 319
Distributional catalogp. 321
Discretep. 321
Univariatep. 321
Multivariatep. 323
Continuousp. 323
Univariatep. 323
Multivariatep. 327
Decision theoryp. 329
Introductionp. 329
Risk and admissibilityp. 330
Unbiased rulesp. 331
Bayes rulesp. 332
Minimax rulesp. 334
Procedure evaluation and other unifying conceptsp. 335
Mean squared errorp. 335
The variance-bias tradeoffp. 335
Other loss functionsp. 336
Generalized absolute lossp. 337
Testing with a distance penaltyp. 337
A threshold loss functionp. 337
Multiplicityp. 338
Multiple testingp. 339
Additive lossp. 339
Non-additive lossp. 340
Exercisesp. 341
Software guidep. 345
Prior elicitationp. 346
Random effects models/Empirical Bayes analysisp. 347
Bayesian analysisp. 351
Special purpose programsp. 352
Teaching programsp. 356
Markov chain Monte Carlo programsp. 357
Answers to selected exercisesp. 363
Referencesp. 381
Author indexp. 407
Subject indexp. 413
Table of Contents provided by Syndetics. All Rights Reserved.

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