Coupling from the past with randomized quasi-Monte Carlo

The coupling-from-the-past (CFTP) algorithm of Propp and Wilson permits one to sample exactly from the stationary distribution of an ergodic Markov chain. By using it n times independently, we obtain an independent sample from that distribution. A more representative sample can be obtained by creating negative dependence between these n replicates; other authors have already proposed to do this via antithetic variates, Latin hypercube sampling, and randomized quasi-Monte Carlo (RQMC). We study a new, often more effective, way of combining CFTP with RQMC, based on the array-RQMC algorithm. We provide numerical illustrations for Markov chains with both finite and continuous state spaces, and compare with the RQMC combinations proposed earlier. (C) 2009 IMACS. Published by Elsevier B.V. All rights reserved.