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.
Publié le : 2011-02-15
Classification:
Metropolis–Hastings algorithm,
Markov chain Monte Carlo (MCMC),
probit model,
central limit theorem,
variance reduction,
conditioning,
62-04,
60F05,
60J22,
60J05,
62B10
@article{1291388375,
author = {Douc, Randal and Robert, Christian P.},
title = {A vanilla Rao--Blackwellization of Metropolis--Hastings algorithms},
journal = {Ann. Statist.},
volume = {39},
number = {1},
year = {2011},
pages = { 261-277},
language = {en},
url = {http://dml.mathdoc.fr/item/1291388375}
}
Douc, Randal; Robert, Christian P. A vanilla Rao–Blackwellization of Metropolis–Hastings algorithms. Ann. Statist., Tome 39 (2011) no. 1, pp. 261-277. http://gdmltest.u-ga.fr/item/1291388375/