Statistical problems in Bayesian decision theory are the focus of this research. The feasibility of applying Gibbs sampling procedures in the evaluation of multi-dimensional integrals for nonparametric Bayesian inference will be evaluated. A decision theoretic approach to classical nonparametric inference will be applied to the problem of estimating the variance of a distribution. The estimation of medians and quantiles will also be explored. Multi-parameter estimation using nonsymmetric loss functions will be studied for the general exponential family as well as the the Poisson distribution.
