Wolpert Laplace Control VariatesLaplace Control Variates : A New

The central computational problem in Bayesian analysis is that of computing the posterior expectation of one or more quantities of interest|a ratio of two often-intractable integrals. The method of Laplace gives an approximation to this ratio that depends only on asymptotic features of the function of interest and the posterior density function, in a neighborhood of the posterior mode. Monte Carlo integration ooers a convergent sequence of numerical approximations to the posterior mean. These two methods have complementary shortcomings: Laplace's method is quick and needs only local information, but may be misleading if the local asymptotics do not reeect the tail behavior of the posterior density or the function of interest; Monte Carlo integration can be slow to converge. Here the two methods are synthesized by using Laplace's method to give a control variable for accelerating the convergence of a Monte Carlo approximation to the integral, with precision estimate.