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.
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