Using Parallel Computation to Improve Independent Metropolis-Hastings Based Estimation

In this paper, we consider the implications of the fact that parallel raw-power canbe exploited by a generic Metropolis{Hastings algorithm if the proposed values areindependent. In particular, we present improvements to the independent Metropolis{Hastings algorithm that signicantly decrease the variance of any estimator derivedfrom the MCMC output, for a null computing cost since those improvements arebased on a xed number of target density evaluations. Furthermore, the techniquesdeveloped in this paper do not jeopardize the Markovian convergence properties of thealgorithm, 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 normalexample and on a classical probit regression model but insist on the fact that they areuniversally applicable.