A vanilla Rao--Blackwellization of Metropolis--Hastings algorithms

Details A vanilla Rao--Blackwellization of Metropolis--Hastings algorithms A vanilla Rao--Blackwellization of Metropolis--Hastings algorithms

2009-04-14

arxiv.org/abs/0904.2144v6

Annals of Statistics 2011, Vol. 39, No. 1, 261-277

Statistics

Computation

Published in at http://dx.doi.org/10.1214/10-AOS838 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

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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