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August 1997 Counterexamples in importance sampling for large deviations probabilities
Paul Glasserman, Yashan Wang
Ann. Appl. Probab. 7(3): 731-746 (August 1997). DOI: 10.1214/aoap/1034801251


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.


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Paul Glasserman. Yashan Wang. "Counterexamples in importance sampling for large deviations probabilities." Ann. Appl. Probab. 7 (3) 731 - 746, August 1997.


Published: August 1997
First available in Project Euclid: 16 October 2002

zbMATH: 0892.60043
MathSciNet: MR1459268
Digital Object Identifier: 10.1214/aoap/1034801251

Primary: 60F10 , 60J15 , 65C05

Keywords: importance sampling , large deviations , Monte Carlo methods , Random walks , Rare events , simulation

Rights: Copyright © 1997 Institute of Mathematical Statistics


Vol.7 • No. 3 • August 1997
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