Preface to the Second Edition | p. xiii |
Preface to the First Edition | p. xv |
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. 17 |
Introduction | p. 17 |
Prior distributions | p. 22 |
Elicited priors | p. 23 |
Conjugate priors | p. 25 |
Noninformative priors | p. 28 |
Other prior construction methods | p. 31 |
Bayesian inference | p. 32 |
Point estimation | p. 32 |
Interval estimation | p. 35 |
Hypothesis testing and Bayes factors | p. 38 |
Example: Consumer preference data | p. 42 |
Model assessment | p. 46 |
Diagnostic measures | p. 46 |
Model averaging | p. 49 |
Nonparametric methods | p. 51 |
Exercises | p. 53 |
The empirical Bayes approach | p. 57 |
Introduction | p. 57 |
Nonparametric EB (NPEB) point estimation | p. 58 |
Compound sampling models | p. 58 |
Simple NPEB (Robbins' method) | p. 59 |
Example: Accident data | p. 60 |
Parametric EB (PEB) point estimation | p. 62 |
Gaussian/Gaussian models | p. 62 |
Beta/binomial model | p. 67 |
EB performance of the PEB | p. 69 |
Stein estimation | p. 70 |
Computation via the EM algorithm | p. 74 |
EM for PEB | p. 74 |
Computing the observed information | p. 76 |
EM for NPEB | p. 77 |
Speeding convergence and generalizations | p. 77 |
Interval estimation | p. 78 |
Morris' approach | p. 79 |
Marginal posterior approach | p. 80 |
Bias correction approach | p. 82 |
Generalization to regression structures | p. 85 |
Exercises | p. 86 |
Performance of Bayes procedures | p. 89 |
Bayesian processing | p. 90 |
Univariate stretching with a two-point prior | p. 90 |
Multivariate Gaussian model | p. 90 |
Frequentist performance: Point estimates | p. 92 |
Gaussian/Gaussian model | p. 92 |
Beta/binomial model | p. 94 |
Generalization | p. 97 |
Frequentist performance: Confidence intervals | p. 98 |
Beta/binomial model | p. 98 |
Fieller-Creasy problem | p. 103 |
Empirical Bayes performance | p. 108 |
Point estimation | p. 108 |
Interval estimation | p. 111 |
Design of experiments | p. 114 |
Bayesian design for frequentist analysis | p. 114 |
Bayesian design for Bayesian analysis | p. 116 |
Exercises | p. 119 |
Bayesian computation | p. 121 |
Introduction | p. 121 |
Asymptotic methods | p. 122 |
Normal approximation | p. 122 |
Laplace's method | p. 124 |
Noniterative Monte Carlo methods | p. 129 |
Direct sampling | p. 129 |
Indirect methods | p. 131 |
Markov chain Monte Carlo methods | p. 137 |
Substitution sampling and data augmentation | p. 137 |
Gibbs sampling | p. 141 |
Metropolis-Hastings algorithm | p. 152 |
Hybrid forms and other algorithms | p. 159 |
Variance estimation | p. 170 |
Convergence monitoring and diagnosis | p. 172 |
Exercises | p. 183 |
Model criticism and selection | p. 193 |
Bayesian robustness | p. 194 |
Sensitivity analysis | p. 194 |
Prior partitioning | p. 199 |
Model assessment | p. 204 |
Bayes factors via marginal density estimation | p. 206 |
Direct methods | p. 207 |
Using Gibbs sampler output | p. 208 |
Using Metropolis-Hastings output | p. 210 |
Bayes factors via sampling over the model space | p. 211 |
Product space search | p. 213 |
"Metropolized" product space search | p. 215 |
Reversible jump MCMC | p. 216 |
Using partial analytic structure | p. 217 |
Other model selection methods | p. 219 |
Penalized likelihood criteria | p. 220 |
Predictive model selection | p. 223 |
Exercises | p. 225 |
Special methods and models | p. 229 |
Estimating histograms and ranks | p. 229 |
Model and inferential goals | p. 230 |
Triple goal estimates | p. 232 |
Smoothing and robustness | p. 234 |
Order restricted inference | p. 237 |
Nonlinear models | p. 239 |
Longitudinal data models | p. 242 |
Continuous and categorical time series | p. 244 |
Survival analysis and frailty models | p. 246 |
Statistical models | p. 246 |
Treatment effect prior determination | p. 247 |
Computation and advanced models | p. 248 |
Sequential analysis | p. 249 |
Model and loss structure | p. 250 |
Backward induction | p. 252 |
Forward sampling | p. 252 |
Spatial and spatio-temporal models | p. 255 |
Point source data models | p. 256 |
Regional summary data models | p. 259 |
Exercises | p. 264 |
Case studies | p. 275 |
Analysis of longitudinal AIDS data | p. 276 |
Introduction and background | p. 276 |
Modeling of longitudinal CD4 counts | p. 277 |
CD4 response to treatment at two months | p. 286 |
Survival analysis | p. 287 |
Discussion | p. 289 |
Robust analysis of clinical trials | p. 290 |
Clinical background | p. 290 |
Interim monitoring | p. 290 |
Prior robustness and prior scoping | p. 295 |
Sequential decision analysis | p. 301 |
Discussion | p. 304 |
Spatio-temporal mapping of lung cancer rates | p. 305 |
Introduction | p. 305 |
Data and model description | p. 307 |
Computational considerations | p. 309 |
Model fitting, validation, and comparison | p. 309 |
Discussion | p. 315 |
Appendices | p. 319 |
Distributional catalog | p. 321 |
Discrete | p. 321 |
Univariate | p. 321 |
Multivariate | p. 323 |
Continuous | p. 323 |
Univariate | p. 323 |
Multivariate | p. 327 |
Decision theory | p. 329 |
Introduction | p. 329 |
Risk and admissibility | p. 330 |
Unbiased rules | p. 331 |
Bayes rules | p. 332 |
Minimax rules | p. 334 |
Procedure evaluation and other unifying concepts | p. 335 |
Mean squared error | p. 335 |
The variance-bias tradeoff | p. 335 |
Other loss functions | p. 336 |
Generalized absolute loss | p. 337 |
Testing with a distance penalty | p. 337 |
A threshold loss function | p. 337 |
Multiplicity | p. 338 |
Multiple testing | p. 339 |
Additive loss | p. 339 |
Non-additive loss | p. 340 |
Exercises | p. 341 |
Software guide | p. 345 |
Prior elicitation | p. 346 |
Random effects models/Empirical Bayes analysis | p. 347 |
Bayesian analysis | p. 351 |
Special purpose programs | p. 352 |
Teaching programs | p. 356 |
Markov chain Monte Carlo programs | p. 357 |
Answers to selected exercises | p. 363 |
References | p. 381 |
Author index | p. 407 |
Subject index | p. 413 |
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