The Annals of Applied Probability

Counterexamples in importance sampling for large deviations probabilities

Paul Glasserman and Yashan Wang

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A guiding principle in the efficient estimation of rare-event probabilities by Monte Carlo is that importance sampling based on the change of measure suggested by a large deviations analysis can reduce variance by many orders of magnitude. In a variety of settings, this approach has led to estimators that are optimal in an asymptotic sense. We give examples, however, in which importance sampling estimators based on a large deviations change of measure have provably poor performance. The estimators can have variance that decreases at a slower rate than a naive estimator, variance that increases with the rarity of the event, and even infinite variance. For each example, we provide an alternative estimator with provably efficient performance. A common feature of our examples is that they allow more than one way for a rare event to occur; our alternative estimators give explicit weight to lower probability paths neglected by leading-term asymptotics.

Article information

Ann. Appl. Probab., Volume 7, Number 3 (1997), 731-746.

First available in Project Euclid: 16 October 2002

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Zentralblatt MATH identifier

Primary: 60F10: Large deviations 60J15 65C05: Monte Carlo methods

Monte Carlo methods rare events random walks large deviations importance sampling simulation


Glasserman, Paul; Wang, Yashan. Counterexamples in importance sampling for large deviations probabilities. Ann. Appl. Probab. 7 (1997), no. 3, 731--746. doi:10.1214/aoap/1034801251.

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