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

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

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August 26, 2009 by Chapman and Hall/CRC
Professional - 344 Pages - 29 B/W Illustrations
ISBN 9781420077490 - CAT# C7749
Series: Chapman & Hall/CRC Biostatistics Series

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Features

  • Presents a wide range of practical missing data problems that are solvable using a Bayesian approach
  • Provides worked out noniterative sampling calculations of posteriors for the problems
  • Uses inverse Bayesian formulae, the EM algorithm, and data augmentation algorithms for computation
  • Illustrates methods with a variety of 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
  • Includes S-PLUS and R computer codes

Summary

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.