Using parallel computation to improve Independent Metropolis--Hastings based estimation
Abstract
In this paper, we consider the implications of the fact that parallel raw-power can be exploited by a generic Metropolis--Hastings algorithm if the proposed values are independent. In particular, we present improvements to the independent Metropolis--Hastings algorithm that significantly decrease the variance of any estimator derived from the MCMC output, for a null computing cost since those improvements are based on a fixed number of target density evaluations. Furthermore, the techniques developed in this paper do not jeopardize the Markovian convergence properties of the algorithm, since they are based on the Rao--Blackwell principles of Gelfand and Smith (1990), already exploited in Casella and Robert (1996), Atchade and Perron (2005) and Douc and Robert (2010). We illustrate those improvements both on a toy normal example and on a classical probit regression model, but stress the fact that they are applicable in any case where the independent Metropolis-Hastings is applicable.
Cite
@article{arxiv.1010.1595,
title = {Using parallel computation to improve Independent Metropolis--Hastings based estimation},
author = {Pierre Jacob and Christian P. Robert and Murray H. Smith},
journal= {arXiv preprint arXiv:1010.1595},
year = {2015}
}
Comments
19 pages, 8 figures, to appear in Journal of Computational and Graphical Statistics