Using parallel computation to improve Independent Metropolis--Hastings based estimation

Pierre Jacob; Christian P. Robert; Murray H. Smith

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arXiv · 1010.1595

Using parallel computation to improve Independent Metropolis--Hastings based estimation

Pierre Jacob·Christian P. Robert·Murray H. Smith

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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.

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BibTeX RIS

Pierre Jacob, Christian P. Robert, Murray H. Smith. 2010-10-08. Using parallel computation to improve Independent Metropolis--Hastings based estimation. https://arxiv.org/abs/1010.1595

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