Journal of Applied Probability

A comparison of cross-entropy and variance minimization strategies

Joshua C. C. Chan, Peter W. Glynn, and Dirk P. Kroese

Abstract

The variance minimization (VM) and cross-entropy (CE) methods are two versatile adaptive importance sampling procedures that have been successfully applied to a wide variety of difficult rare-event estimation problems. We compare these two methods via various examples where the optimal VM and CE importance densities can be obtained analytically. We find that in the cases studied both VM and CE methods prescribe the same importance sampling parameters, suggesting that the criterion of minimizing the CE distance is very close, if not asymptotically identical, to minimizing the variance of the associated importance sampling estimator.

Article information

Source
J. Appl. Probab., Volume 48A (2011), 183-194.

Dates
First available in Project Euclid: 18 October 2011

Permanent link to this document
https://projecteuclid.org/euclid.jap/1318940464

Digital Object Identifier
doi:10.1239/jap/1318940464

Mathematical Reviews number (MathSciNet)
MR2865625

Zentralblatt MATH identifier
1241.65021

Subjects
Primary: 65C05: Monte Carlo methods
Secondary: 65C60: Computational problems in statistics

Keywords
Variance minimization cross entropy importance sampling rare-event simulation likelihood ratio degeneracy

Citation

Chan, Joshua C. C.; Glynn, Peter W.; Kroese, Dirk P. A comparison of cross-entropy and variance minimization strategies. J. Appl. Probab. 48A (2011), 183--194. doi:10.1239/jap/1318940464. https://projecteuclid.org/euclid.jap/1318940464


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