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Counterexamples in Importance Sampling for Large Deviations Probabilities
Paul Glasserman and Yashan Wang
The Annals of Applied Probability
Vol. 7, No. 3 (Aug., 1997), pp. 731-746
Published by: Institute of Mathematical Statistics
Stable URL: http://www.jstor.org/stable/2245293
Page Count: 16
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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 probably 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.
The Annals of Applied Probability © 1997 Institute of Mathematical Statistics