Parallel and interacting Markov chain Monte Carlo algorithm

Authors:
Fabien Campillo;Rivo Rakotozafy;Vivien Rossi
Affiliations:
INRIA/INRA, MERE Project-Team, Montpellier, France;University of Fianarantsoa, Fianarantsoa, Madagascar;CIRAD, Research Unit, Dynamics of Natural Forests, Montpellier, France
Venue:
Mathematics and Computers in Simulation
Year:
2009

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Abstract

In many situations it is important to be able to propose N independent realizations of a given distribution law. We propose a strategy for making N parallel Monte Carlo Markov chains (MCMC) interact in order to get an approximation of an independent N-sample of a given target law. In this method each individual chain proposes candidates for all other chains. We prove that the set of interacting chains is itself a MCMC method for the product of N target measures. Compared to independent parallel chains this method is more time consuming, but we show through examples that it possesses many advantages. This approach is applied to a biomass evolution model.