Casella and Robert [Biometrika 83 (1996) 81–94] presented a general Rao–Blackwellization principle for accept-reject and Metropolis–Hastings schemes that leads to significant decreases in the variance of the resulting estimators, but at a high cost in computation and storage. Adopting a completely different perspective, we introduce instead a universal scheme that guarantees variance reductions in all Metropolis–Hastings-based estimators while keeping the computation cost under control. We establish a central limit theorem for the improved estimators and illustrate their performances on toy examples and on a probit model estimation.
"A vanilla Rao–Blackwellization of Metropolis–Hastings algorithms." Ann. Statist. 39 (1) 261 - 277, February 2011. https://doi.org/10.1214/10-AOS838