Bayesian Missing Data Problems: EM, Data Augmentation and Noniterative Computation

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Ming T. Tan Guo-Liang Tian

Bayesian Missing Data Problems

EM, Data Augmentation and Noniterative Computation

Ming T. Tan, Guo-Liang Tian, Kai Wang Ng

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English

Chapman & Hall/CRC
26 August 2009

Probability & statistics; Biology, life sciences

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.

By: Ming T. Tan, Guo-Liang Tian, Kai Wang Ng
Imprint: Chapman & Hall/CRC
Country of Publication: United Kingdom
Volume: v. 32
Dimensions: Height: 234mm, Width: 156mm, Spine: 23mm
Weight: 635g
ISBN: 9781420077490
ISBN 10: 142007749X
Pages: 346
Publication Date: 26 August 2009
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

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.

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.

Reviews for Bayesian Missing Data Problems: EM, Data Augmentation and Noniterative Computation

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