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The assessment of the probability of a rare event with a naive Monte-Carlomethod is computationally intensive, so faster estimation or variance reductionmethods are needed. We focus on one of these methods which is the interactingparticle system (IPS) method. The method is not intrusive in the sense that therandom Markov system under consideration is simulated with its originaldistribution, but selection steps are introduced that favor trajectories(particles) with high potential values. An unbiased estimator with reducedvariance can then be proposed. The method requires to specify a set ofpotential functions. The choice of these functions is crucial, because itdetermines the magnitude of the variance reduction. So far, little informationwas available on how to choose the potential functions. This paper provides theexpressions of the optimal potential functions minimizing the asymptoticvariance of the estimator of the IPS method and it proposes recommendations forthe practical design of the potential functions.

Optimal input potential functions in the interacting particle system method