Preface to the Second Edition
Preface to the First Edition
1
Approaches for statistical inference
1.1 Introduction
1.2
Motivating vignettes
1.2.1
Personal probability
1.2.2 Missing data
1.2.3 Bioassay
1.2.4 Attenuation adjustment
1.3
Defining the approaches
1.4
The Bayes-frequentist controversy
1.5
Some basic Bayesian models
1.5.1
A Gaussian/Gaussian (normal/normal) model
1.5.2
A beta/binomial model
1.6 Exercises
2 The Bayes approach
2.1 Introduction
2.2
Prior distributions
2.2.1
Elicited priors
2.2.2
Conjugate priors
2.2.3
Noninformative priors
2.2.4 Other prior construction methods
2.3
Bayesian inference
2.3.1
Point estimation
2.3.2 Interval estimation
2.3.3
Hypothesis testing and Bayes factors
2.3.4 Example: Consumer preference data
2.4 Model assessment
2.4.1
Diagnostic measures
© 2000 by CRC Press LLC
2.4.2 Model averaging
2.5 Nonparametric methods
2.6 Exercises
3 The empirical Bayes approach
3.1 Introduction
3.2
Nonparametric EB (NPEB) point estimation
3.2.1
Compound sampling models
3.2.2 Simple NPEB (Robbins' method)
3.2.3 Example: Accident data
3.3
Parametric EB (PEB) point estimation
3.3.1
Gaussian/Gaussian models
3.3.2
Beta/binomial model
3.3.3
EB performance of the PEB
3.3.4 Stein estimation
3.4
Computation via the EM algorithm
3.4.1
EM for PEB
3.4.2
Computing the observed information
3.4.3 EM for NPEB
3.4.4 Speeding convergence and generalizations
3.5
Interval estimation
3.5.1 Morris' approach
3.5.2
Marginal posterior approach
3.5.3 Bias correction approach
3.6
Generalization to regression structures
3.7 Exercises
4 Performance of Bayes procedures
4.1
Bayesian processing
4.1.1
Univariate stretching with a two-point prior
4.1.2
Multivariate Gaussian model
4.2
Frequentist performance: Point estimates
4.2.1
Gaussian/Gaussian model
4.2.2
Beta/binomial model
4.2.3 Generalization
4.3 Frequentist performance: Confidence intervals
4.3.1
Beta/binomial model
4.3.2 Fieller-Creasy problem
4.4
Empirical Bayes performance
4.4.1 Point estimation
4.4.2 Interval estimation
4.5
Design of experiments
4.5.1
Bayesian design for frequentist analysis
4.5.2
Bayesian design for Bayesian analysis
© 2000 by CRC Press LLC
4.6 Exercises
5 Bayesian computation
5.1 Introduction
5.2
Asymptotic methods
5.2.1
Normal approximation
5.2.2
Laplace's method
5.3
Noniterative Monte Carlo methods
5.3.1 Direct sampling
5.3.2 Indirect methods
5.4
Markov chain Monte Carlo methods
5.4.1
Substitution sampling and data augmentation
5.4.2
Gibbs sampling
5.4.3 Metropolis-Hastings algorithm
5.4.4
Hybrid forms and other algorithms
5.4.5 Variance estimation
5.4.6
Convergence monitoring and diagnosis
5.5 Exercises
6
Model criticism and selection
6.1
Bayesian robustness
6.1.1 Sensitivity analysis
6.1.2 Prior partitioning
6.2
Model assessment
6.3
Hayes factors via marginal density estimation
6.3.1 Direct methods
6.3.2
Using Gibbs sampler output
6.3.3
Using Metropolis-Hastings output
6.4
Bayes factors via sampling over the model space
6.4.1
Product space search
6.4.2
"Metropolized" product space search
6.4.3
Reversible jump MCMC
6.4.4
Using partial analytic structure
6.5
Other model selection methods
6.5.1
Penalized likelihood criteria
6.5.2
Predictive model selection
6.6 Exercises
7 Special methods and models
7.1
Estimating histograms and ranks
7.1.1
Model and inferential goals
7.1.2
Triple goal estimates
7.1.3
Smoothing and robustness
7.2
Order restricted inference
© 2000 by CRC Press LLC
7.3
Nonlinear models
7.4
Longitudinal data models
7.5
Continuous and categorical time series
7.6
Survival analysis and frailty models
7.6.1 Statistical models
7.6.2 Treatment effect prior determination
7.6.3
Computation and advanced models
7.7
Sequential analysis
7.7.1
Model and loss structure
7.7.2 Backward induction
7.7.3
Forward sampling
7.8
Spatial and spatio-temporal models
7.8.1
Point source data models
7.8.2
Regional summary data models
7.9 Exercises
8 Case studies
8.1
Analysis of longitudinal AIDS data
8.1.1 Introduction and background
8.1.2
Modeling of longitudinal CD4 counts
8.1.3 CD4 response to treatment at two months
8.1.4 Survival analysis
8.1.5 Discussion
8.2
Robust analysis of clinical trials
8.2.1
Clinical background
8.2.2 Interim monitoring
8.2.3
Prior robustness and prior scoping
8.2.4 Sequential decision analysis
8.2.5 Discussion
8.3
Spatio-temporal mapping of lung cancer rates
8.3.1 Introduction
8.3.2
Data and model description
8.3.3
Computational considerations
8.3.4
Model fitting, validation, and comparison
8.3.5 Discussion
Appendices
A Distributional catalog
A.1 Discrete
A.1.1 Univariate
A.1.2 Multivariate
A.2 Continuous
A.2.1 Univariate
© 2000 by CRC Press LLC
A.2.2 Multivariate
B Decision theory
B.1 Introduction
B.1.1 Risk and admissibility
B.1.2 Unbiased rules
B.1.3 Bayes rules
B.1.4 Minimax rules
B.2 Procedure evaluation and other unifying concepts
B.2.1 Mean squared error
B.2.2 The variance-bias tradeoff
B.3 Other loss functions
B.3.1 Generalized absolute loss
B.3.2 Testing with a distance penalty
B.3.3 A threshold loss function
B.4 Multiplicity
B.5 Multiple testing
B.5.1 Additive loss
B.5.2 Non-additive loss
B.6 Exercises
C Software guide
C.1 Prior elicitation
C.2 Random effects models/ Empirical Bayes analysis
C.3 Bayesian analysis
C.3.1 Special purpose programs
C.3.2 Teaching programs
C.3.3 Markov chain Monte Carlo programs
D Answers to selected exercises
References
© 2000 by CRC Press LLC
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