Zero Variance Markov Chain Monte Carlo for Bayesian Estimators

A general purpose variance reduction technique for Markov chain Monte Carlo estimators based on the zero-variance principle introduced in the physics literature by Assaraf and Caffarel (1999, 2003), is proposed. Conditions for unbiasedness of the zero-variance estimator are derived. A central limit theorem is also proved under regularity conditions. The potential of the new idea is illustrated with real applications to Bayesian inference for probit, logit and GARCH models.