State-dependent importance sampling schemes via minimum cross-entropy

A.A.N. Ridder, T. Taimre

Research output: Contribution to JournalArticleAcademicpeer-review

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. © 2009 The Author(s).
Original languageEnglish
Pages (from-to)357-388
JournalAnnals of Operations Research
Volume189
Issue number1
DOIs
Publication statusPublished - 2011

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Importance sampling
Estimator
Cross-entropy
Simulation
Jump

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title = "State-dependent importance sampling schemes via minimum cross-entropy",
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. {\circledC} 2009 The Author(s).",
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State-dependent importance sampling schemes via minimum cross-entropy. / Ridder, A.A.N.; Taimre, T.

In: Annals of Operations Research, Vol. 189, No. 1, 2011, p. 357-388.

Research output: Contribution to JournalArticleAcademicpeer-review

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T1 - State-dependent importance sampling schemes via minimum cross-entropy

AU - Ridder, A.A.N.

AU - Taimre, T.

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AB - 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. © 2009 The Author(s).

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DO - 10.1007/s10479-009-0611-7

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SP - 357

EP - 388

JO - Annals of Operations Research

JF - Annals of Operations Research

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