Bayesian Methods for Data Analysis

✍ Scribed by Bradley P. Carlin, Thomas A. Louis

• Publisher: Chapman and Hall/CRC
• Year: 2008
• Tongue: English
• Leaves: 538
• Series: Texts in Statistical Science 78
• Edition: 3
• Category: Library

✦ Synopsis

Broadening its scope to nonstatisticians, Bayesian Methods for Data Analysis, Third Edition provides an accessible introduction to the foundations and applications of Bayesian analysis. Along with a complete reorganization of the material, this edition concentrates more on hierarchical Bayesian modeling as implemented via Markov chain Monte Carlo (MCMC) methods and related data analytic techniques.

New to the Third Edition

New data examples, corresponding R and WinBUGS code, and homework problems

Explicit descriptions and illustrations of hierarchical modeling―now commonplace in Bayesian data analysis

A new chapter on Bayesian design that emphasizes Bayesian clinical trials

A completely revised and expanded section on ranking and histogram estimation

A new case study on infectious disease modeling and the 1918 flu epidemic

A solutions manual for qualifying instructors that contains solutions, computer code, and associated output for every homework problem―available both electronically and in print

Ideal for Anyone Performing Statistical Analyses

Focusing on applications from biostatistics, epidemiology, and medicine, this text builds on the popularity of its predecessors by making it suitable for even more practitioners and students.

✦ Table of Contents

Cover Page
Half Title Page
CHAPMAN & HALL/CRC
Title Page
Copyright Page
Dedication
Contents
Preface to the Third Edition
CHAPTER 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
CHAPTER 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
2.4 Hierarchical modeling
2.4.1 Normal linear models
2.4.2 Effective model size and the DIC criterion
2.5 Model assessment
2.5.1 Diagnostic measures
2.5.2 Model averaging
2.6 Nonparametric methods
2.7 Exercises
CHAPTER 3. Bayesian computation
3.1 Introduction
3.2 Asymptotic methods
3.2.1 Normal approximation
3.3 Noniterative Monte Carlo methods
3.3.1 Direct sampling
3.3.2 Indirect methods
3.4 Markov chain Monte Carlo methods
3.4.1 Gibbs sampler
3.4.2 Metropolis-Hastings algorithm
3.4.3 Slice sampler
3.4.4 Hybrid forms, adaptive MCMC, and other algorithms
3.4.5 Variance estimation
3.4.6 Convergence monitoring and diagnosis
3.5 Exercises
CHAPTER 4. Model criticism and selection
4.1 Bayesian modeling
4.1.1 Linear models
4.1.2 Nonlinear models
4.1.3 Binary data models
4.2 Bayesian robustness
4.2.1 Sensitivity analysis
4.2.2 Prior partitioning
4.3 Model assessment
4.4 Bayes factors via marginal density estimation
4.4.1 Direct methods
4.4.2 Using Gibbs sampler output
4.4.3 Using Metropolis-Hastings output
4.5 Bayes factors via sampling over the model space
4.5.1 Product space search
4.5.2 “Metropolized” product space search
4.5.3 Reversible jump MCMC
4.5.4 Using partial analytic structure
4.6 Other model selection methods
4.6.1 Penalized likelihood criteria: AIC, BIC, and DIC
4.6.2 Predictive model selection
4.7 Exercises
CHAPTER 5. The empirical Bayes approach
5.1 Introduction
5.2 Parametric EB (PEB) point estimation
5.2.1 Gaussian/Gaussian models
5.2.2 Computation via the EM algorithm
5.2.3 EB performance of the PEB
5.2.4 Stein estimation
5.3 Nonparametric EB (NPEB) point estimation
5.3.1 Compound sampling models
5.4 Interval estimation
5.4.1 Morris’ approach
5.4.2 Marginal posterior approach
5.4.3 Bias correction approach
5.5 Bayesian processing and performance
5.5.1 Univariate stretching with a two-point prior
5.5.2 Multivariate Gaussian model
5.6 Frequentist performance
5.6.1 Gaussian/Gaussian model
5.6.2 Beta/binomial model
5.7 Empirical Bayes performance
5.7.1 Point estimation
5.7.2 Interval estimation
5.8 Exercises
CHAPTER 6. Bayesian design
6.1 Principles of design
6.1.1 Bayesian design for frequentist analysis
6.1.2 Bayesian design for Bayesian analysis
6.2 Bayesian clinical trial design
6.2.1 Classical versus Bayesian trial design
6.2.2 Bayesian assurance
6.2.3 Bayesian indifference zone methods
6.2.4 Other Bayesian approaches
6.2.5 Extensions
6.3 Applications in drug and medical device trials
6.3.1 Binary endpoint drug trial
6.3.2 Cox regression device trial with interim analysis
6.4 Exercises
CHAPTER 7. Special methods and models
7.1 Estimating histograms and ranks
7.1.1 Bayesian ranking
7.1.2 Histogram and triple goal estimates
7.1.3 Robust prior distributions
7.2 Order restricted inference
7.3 Longitudinal data models
7.4 Continuous and categorical time series
7.5 Survival analysis and frailty models
7.5.1 Statistical models
7.5.2 Treatment effect prior determination
7.5.3 Computation and advanced models
7.6 Sequential analysis
7.6.1 Model and loss structure
7.6.2 Backward induction
7.6.3 Forward sampling
7.7 Spatial and spatio-temporal models
7.7.1 Point source data models
7.7.2 Regional summary data models
7.8 Exercises
CHAPTER 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 Modeling of infectious diseases
8.3.1 Introduction and data
8.3.2 Stochastic compartmental model
8.3.3 Parameter estimation and model building
8.3.4 Results
8.3.5 Discussion
Appendices
APPENDIX A. Distributional catalog
A.1 Discrete
A.1.1 Univariate
A.1.2 Multivariate
A.2 Continuous
A.2.1 Univariate
A.2.2 Multivariate
APPENDIX 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 (MSE)
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
APPENDIX C. Answers to selected exercises
References
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