Journal of Applied Probability

A comparison of cross-entropy and variance minimization strategies

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


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

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

First available in Project Euclid: 18 October 2011

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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