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.
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.
Introduction Background Scope, Aim and Outline Inverse Bayes Formulae (IBF) The Bayesian Methodology The Missing Data Problems Entropy Optimization, Monte Carlo Simulation and Numerical Integration Optimization Monte Carlo Simulation Numerical Integration Exact Solutions 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 x 2 Crossover Trial with Missing Data Hierarchical Models 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 Changepoint Problems Capture-Recapture 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 Remarks Constrained Parameter Problems Linear Inequality Constraints Constrained Normal Models Constrained Poisson Models Constrained Binomial Models Checking Compatibility and Uniqueness Introduction 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 Discrete Distributions Continuous Distributions Mixture Distributions Stochastic Processes References Author Index Subject Index Problems appear at the end of each chapter.
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