Bayesian Missing Data Problems

This book provides a systematic view of Bayesian methods to be used with missing data problems. The text presents a non-iterative approach that provides either explicit or non-iterative sampling calculation of posteriors. This computation includes exact numerical solutions, a conditional sampling approach via data augmentation, and a non-iterative sampling approach via EM-type algorithms. It illustrates the application of Bayesian analysis to important biostatistics problems and to other real-world applications, including the constrained parameter problem reformulated as a missing data problem.. The text includes S-PLUS/R computer codes to supplement existing functions for statistical distributions and stochastic processes

Presents solutions to missing data problems through explicit or noniterative sampling calculation of Bayesian posteriors, based on the inverse Bayes formulae. This work focuses on exact numerical solutions, a conditional sampling approach via data augmentation, and a noniterative sampling approach via EM-type algorithms.

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.