Monte Carlo Approximations in Bayesian Decision Theory. Part 3. Limiting Behavior of Monte Carlo Approximations

摘要

Monte Carlo approximation is a useful method in obtaining a numerical approximation to a Bayesian action (an action which minimizes the posterior expected loss). We study the behavior of the Monte Carlo approximation when the Monte Carlo sample size is large. Convergence and convergence rate of the Monte Carlo approximation are established under some weak conditions on the loss function. (kr)