Using parallel computation to improve Independent Metropolis-Hastings based estimation

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

Smith, Murray H.; Robert, Christian P.; Jacob, Pierre E. (2011), Using parallel computation to improve Independent Metropolis-Hastings based estimation, Journal of Computational and Graphical Statistics, 20, 3, p. 616-635. http://dx.doi.org/10.1198/jcgs.2011.10167

Type

Article accepté pour publication ou publié

External document link

http://fr.arXiv.org/abs/1010.1595

Date

2011

Journal name

Journal of Computational and Graphical Statistics

Volume

Number

Publisher

American Statistical Association

Pages

616-635

Abstract (EN)

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.

Subjects / Keywords

Metropolis-Hastings algorithm