A vanilla Rao–Blackwellization of Metropolis–Hastings algorithms

The Annals of Statistics · 2011 · Volume 39 · Issue 1

Abstract

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.

Keywords

60F05, 60J05, 60J22, 62-04, 62B10, central limit theorem, Conditioning, Markov chain Monte Carlo (MCMC), Metropolis–Hastings algorithm, probit model, variance reduction

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