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February 2011 A vanilla Rao–Blackwellization of Metropolis–Hastings algorithms
Randal Douc, Christian P. Robert
Ann. Statist. 39(1): 261-277 (February 2011). DOI: 10.1214/10-AOS838


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.


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Randal Douc. Christian P. Robert. "A vanilla Rao–Blackwellization of Metropolis–Hastings algorithms." Ann. Statist. 39 (1) 261 - 277, February 2011.


Published: February 2011
First available in Project Euclid: 3 December 2010

zbMATH: 1209.62023
MathSciNet: MR2797846
Digital Object Identifier: 10.1214/10-AOS838

Primary: 60F05 , 60J05 , 60J22 , 62-04 , 62B10

Keywords: central limit theorem , Conditioning , Markov chain Monte Carlo (MCMC) , Metropolis–Hastings algorithm , probit model , variance reduction

Rights: Copyright © 2011 Institute of Mathematical Statistics


Vol.39 • No. 1 • February 2011
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