Using parallel computation to improve Independent Metropolis-Hastings based estimation. Jacob, P., Robert, C. P, & Smith, M. H arXiv, stat.CO, 2010.
abstract   bibtex   
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 improvement both on a toy normal example and on a classical probit regression model but insist on the fact that they are universally applicable.
@Article{Jacob2010,
author = {Jacob, Pierre and Robert, Christian P and Smith, Murray H}, 
title = {Using parallel computation to improve Independent Metropolis-Hastings based estimation}, 
journal = {arXiv}, 
volume = {stat.CO}, 
number = {}, 
pages = {}, 
year = {2010}, 
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 improvement both on a toy normal example and on a classical probit regression model but insist on the fact that they are universally applicable.}, 
location = {Universite Paris-Dauphine and CREST, France}, 
keywords = {cs.DC; cs.DS; stat.CO}}
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