Sampling-resampling techniques for the computation of posterior densities in normal means problems

Summary Implementation of Bayesian methods is complicated in many contexts by the apparent need for specialized numerical integration techniques, unfamiliar to most statistical practitioners. In fact, a shift of focus to a sampling-resampling perspective enables one to carry out Bayesian calculations without recourse to numerical integration. Such an approach is illustrated here in the familiar context of normal means inference problems, with particular focus on implementing analyses with reference priors.