Bayesian Missing Data Problems: EM, Data Augmentation and Noniterative Computation presents solutions to missing data problems through explicit or noniterative sampling calculation of Bayesian posteriors. The methods are based on the inverse Bayes formulae discovered by one of the author in 1995. Applying the Bayesian approach to important real-world problems, the authors focus on exact numerical solutions, a conditional sampling approach via data augmentation, and a noniterative sampling approach via EM-type algorithms.
After introducing the missing data problems, Bayesian approach, and posterior computation, the book succinctly describes EM-type algorithms, Monte Carlo simulation, numerical techniques, and optimization methods. It then gives exact posterior solutions for problems, such as nonresponses in surveys and cross-over trials with missing values. It also provides noniterative posterior sampling solutions for problems, such as contingency tables with supplemental margins, aggregated responses in surveys, zero-inflated Poisson, capture-recapture models, mixed effects models, right-censored regression model, and constrained parameter models. The text concludes with a discussion on compatibility, a fundamental issue in Bayesian inference.
This book offers a unified treatment of an array of statistical problems that involve missing data and constrained parameters. It shows how Bayesian procedures can be useful in solving these problems.
Scope, Aim and Outline
Inverse Bayes Formulae (IBF)
The Bayesian Methodology
The Missing Data Problems
Optimization, Monte Carlo Simulation and Numerical Integration
Monte Carlo Simulation
Sample Surveys with Nonresponse
Misclassified Multinomial Model
Genetic Linkage Model
Weibull Process with Missing Data
Prediction Problem with Missing Data
Binormal Model with Missing Data
The 2 × 2 Crossover Trial with Missing Data
Nonproduct Measurable Space (NPMS)
Discrete Missing Data Problems
The Exact IBF Sampling
Genetic Linkage Model
Contingency Tables with One Supplemental Margin
Contingency Tables with Two Supplemental Margins
The Hidden Sensitivity Model for Surveys with Two Sensitive Questions
Zero-Inflated Poisson Model
Computing Posteriors in the EM-Type Structures
The IBF Method
Incomplete Pro-Post Test Problems
Right Censored Regression Model
Linear Mixed Models for Longitudinal Data
Probit Regression Models for Independent Binary Data
A Probit-Normal GLMM for Repeated Binary Data
Hierarchical Models for Correlated Binary Data
Hybrid Algorithms: Combining the IBF Sampler with the Gibbs Sampler
Assessing Convergence ofMCMC Methods
Constrained Parameter Problems
Linear Inequality Constraints
Constrained Normal Models
Constrained Poisson Models
Constrained Binomial Models
Checking Compatibility and Uniqueness
Two Continuous Conditional Distributions: Product Measurable Space (PMS)
Finite Discrete Conditional Distributions: PMS
Two Conditional Distributions: NPMS
One Marginal and Another Conditional Distribution
Appendix: Basic Statistical Distributions and Stochastic Processes
Problems appear at the end of each chapter.
Ming T. Tan is Professor of Biostatistics in the Department of Epidemiology and Preventive Medicine at the University of Maryland School of Medicine and Director of the Division of Biostatistics at the University of Maryland Greenebaum Cancer Center.
Guo-Liang Tian is Associate Professor in the Department of Statistics and Actuarial Science at the University of Hong Kong.
Kai Wang Ng is Professor and Head of the Department of Statistics and Actuarial Science at the University of Hong Kong.
In Bayesian Missing Data Problems, the authors provide a new and appealing approach to handle missing data problems (MDPs), based on noniterative methods. … the examples and real applications following key theorems and concepts are useful for readers to further understand the results and pinpoint major advantages or drawbacks about the proposed methodology. … I recommend this book as a valuable reference for researchers interested in MDPs, and I believe that the methodology described in the book should be included in the up-to-date literature on missing data. … the book stimulated my interest, suggesting an alternative way to think about MDPs. …
—Biometrics, June 2011
… [this book] sits nicely alongside Tanner’s Tools for Statistical Inference. … For those interested in Bayesian computational methods, this book will be of great interest. …
—International Statistical Review (2010), 78, 3