Mathematical Sciences: Investigations in Bayesian Analysis, Statistical Decision Theory and Computation

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The research supported on this project falls within three related areas of statistics: Bayesian analysis, statistical decision theory, and computation. The research in Bayesian analysis includes robust Bayesian analysis (in particular, sensitivity to the prior and the loss), Bayesian design, hierarchical Bayesian estimation and selection, testing of lower dimensional hypotheses and robust testing, density estimation, noninformative and reference prior development for "automatic" Bayesian methodology, and elimination of nuisance parameters. Within the statistical decision theory, the research involves multivariate estimation (with emphasis on covariance matrix and discriminant function estimation), empirical Bayes and robust Bayes selection procedures, and sequential and multi-stage selection procedures. The computational problems include Monte Carlo integration for Bayesian calculation and generation of random variables.