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.
Publié le : 1997-08-14
Classification:
Monte Carlo methods,
rare events,
random walks,
large deviations,
importance sampling,
simulation,
60F10,
60J15,
65C05
@article{1034801251,
author = {Glasserman, Paul and Wang, Yashan},
title = {Counterexamples in importance sampling for large deviations
probabilities},
journal = {Ann. Appl. Probab.},
volume = {7},
number = {1},
year = {1997},
pages = { 731-746},
language = {en},
url = {http://dml.mathdoc.fr/item/1034801251}
}
Glasserman, Paul; Wang, Yashan. Counterexamples in importance sampling for large deviations
probabilities. Ann. Appl. Probab., Tome 7 (1997) no. 1, pp. 731-746. http://gdmltest.u-ga.fr/item/1034801251/