Coupling from the past with randomized quasi-Monte Carlo |
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Authors: | P L’Ecuyer C Sanvido |
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Affiliation: | DIRO, Université de Montréal, CP 6128, Succ. Centre-Ville, Montréal H3C 3J7, Canada |
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Abstract: | 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. |
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Keywords: | Variance reduction Randomized quasi-Monte Carlo Markov chain Perfect sampling Coupling from the past |
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