Mathematical Sciences: Some Problems in Bayesian Statistics
Albert Lo Principal Investigator
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This research involves problems in Bayesian nonparametric statistics. The Bayesian statistical theory will be advanced for unimodal and symmetric density and monotone failure rate models. Furthermore, computing procedures will be developed to allow these methods to be applied to realistic data. A second problem involves statistics on a sphere for a rotationally symmetric model. In this setting a Bayes method for directional data is provided for the cases of large samples and small samples. In a third problem, the large sample properties of the posterior distribution of a parameter are studied in the presence of partial information. The last problem concerns the accuracy of the finite (or infinite) Bayesian bootstrap approximation to posterior distributions with respect to smooth prior distributions and the sampling distribution of a corresponding statistic.