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

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This team will work in four areas: decision theory, Bayesian analysis, probability, and computation. The decision- theoretic problems to be considered include multivariate estimation, the development of estimated loss methodology, ranking and selection for both classical and hierarchical Bayesian models, sequential decision problems and adaptive estimation and testing. Problems in Bayesian analysis that will be addressed include the development of robust Bayesian methods for testing of precise hypotheses, hierarchical Baysian analysis, density and function estimation, and the development of noninformative priors. Within probability theory and sequential analysis, problems to be considered include study of branching diffusions, investigation of one-dimensional Gibbs states, sequential methods in survival analysis, and certain problems in distribution theory. Finally, the computational problems to be considered include Bayesian calculation via quadrature, Monte Carlo, and approximations, generation of random variables, and related problems of density simulation. This research team will work on a broad spectrum of problems in statistics and probability, the solutions to which will provide more efficient and more comprehensive methods for producing information, extracting information from data and making informed decisions. Overcoming computational problems is a requirement for progress on some of these fronts.