A vanilla Rao--Blackwellization of Metropolis--Hastings algorithms
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.
Cite
@article{arxiv.0904.2144,
title = {A vanilla Rao--Blackwellization of Metropolis--Hastings algorithms},
author = {Randal Douc and Christian P. Robert},
journal= {arXiv preprint arXiv:0904.2144},
year = {2011}
}
Comments
Published in at http://dx.doi.org/10.1214/10-AOS838 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)