Antithetic Acceleration of Monte Carlo Integration in Bayesian Inference

Abstract

It is proposed to sample antithetically rather than randomly from the posterior density in Bayesian inference using Monte Carlo integration. Conditions are established under which the number of replications required with antithetic sampling relative to the number required with random sampling is inversely proportional to sample size, as sample size increases. The result is illustrated in an experiment using a bivariate vector autoregression.