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.