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Randomized quasi-Monte Carlo for Markov Chains

Friday 3rd November 2006 - 15:45 to 17:00
INI Seminar Room 1

Quasi-Monte Carlo (QMC) methods are numerical techniques for estimating large-dimensional integrals, usually over the unit hypercube. They can be applied, at least in principle, to any stochastic simulation whose aim is to estimate a mathematical expectation. This covers a wide range of applications. Practical error bounds are hard to obtain with QMC but randomized quasi-Monte Carlo (RQMC) permits one to compute an unbiased estimator of the integral, together with a confidence interval. RQMC can in fact be viewed as a variance-reduction technique.

In this talk, we review some key ideas of RQMC methods and provide concrete examples of their application to simulate systems modeled as Markov chains. We also present a new RQMC method, called array-RQMC, recently introduced to simulate Markov chains over a large number of steps. Our numerical illustrations indicate that RQMC can dramatically reduce the variance compared with standard Monte Carlo.

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons