Markov chain importance sampling with applications to rare event probability estimation

Authors:
Zdravko I. Botev;Pierre L'Ecuyer;Bruno Tuffin
Affiliations:
School of Mathematics and Statistics, University of New South Wales, Sydney, Australia 2052;Department of Computer Science and Operations Research, Université de Montréal, Montréal, Canada H3C 3J7;INRIA Rennes Bretagne-Atlantique, Rennes Cedex, France 35042
Venue:
Statistics and Computing
Year:
2013

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Abstract

We present a versatile Monte Carlo method for estimating multidimensional integrals, with applications to rare-event probability estimation. The method fuses two distinct and popular Monte Carlo simulation methods--Markov chain Monte Carlo and importance sampling--into a single algorithm. We show that for some applied numerical examples the proposed Markov Chain importance sampling algorithm performs better than methods based solely on importance sampling or MCMC.