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State-dependent importance sampling schemes via minimum cross-entropy

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  • Ad Ridder
  • Thomas Taimre

Abstract

We present a method to obtain state- and time-dependent importance sampling estimators by repeatedly solving a minimum cross-entropy (MCE) program as the simulation progresses. This MCE-based approach lends a foundation to the natural notion to stop changing the measure when it is no longer needed. We use this method to obtain a state- and time-dependent estimator for the one-tailed probability of a light-tailed i.i.d. sum that is logarithmically efficient in general and strongly efficient when the jumps are Gaussian. We go on to construct an estimator for the two-tailed problem which is shown to be similarly efficient. We consider minor variants of the algorithm obtained via MCE, and present some numerical comparisons between our algorithms and others from the literature. Copyright The Author(s) 2011

Suggested Citation

  • Ad Ridder & Thomas Taimre, 2011. "State-dependent importance sampling schemes via minimum cross-entropy," Annals of Operations Research, Springer, vol. 189(1), pages 357-388, September.
    • Handle: RePEc:spr:annopr:v:189:y:2011:i:1:p:357-388:10.1007/s10479-009-0611-7
    DOI: 10.1007/s10479-009-0611-7
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    References listed on IDEAS

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    1. Paul Dupuis & Hui Wang, 2007. "Subsolutions of an Isaacs Equation and Efficient Schemes for Importance Sampling," Mathematics of Operations Research, INFORMS, vol. 32(3), pages 723-757, August.
    2. R. Y. Rubinstein, 2005. "A Stochastic Minimum Cross-Entropy Method for Combinatorial Optimization and Rare-event Estimation," Methodology and Computing in Applied Probability, Springer, vol. 7(1), pages 5-50, March.
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