This book presents solutions to missing data problems through explicit or noniterative sampling calculation of Bayesian posteriors, based on the inverse Bayes formulae. The authors focus on exact numerical solutions, a conditional sampling approach via data augmentation, and a noniterative sampling approach via EM-type algorithms. They describe Monte Carlo simulation, numerical techniques, and optimization methods. The book illustrates the methods with biostatistical models and real-world applications, including mixed effects and hierarchical models, nonresponse and contingency tables, and the constrained parameter problem reformulated as a missing data problem.

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. Optimization, Monte Carlo Simulation and Numerical Integration. Exact Solutions. Discrete Missing Data Problems. Computing Posteriors in the EM-Type Structures. Constrained Parameter Problems. Checking Compatibility and Uniqueness. Appendix. References. Indices.