State-dependent importance sampling schemes via minimum cross-entropy

Ridder, Ad and Taimre, Thomas (2011) State-dependent importance sampling schemes via minimum cross-entropy. Annals of Operations Research, 189 1: 357-388. doi:10.1007/s10479-009-0611-7


Author Ridder, Ad
Taimre, Thomas
Title State-dependent importance sampling schemes via minimum cross-entropy
Journal name Annals of Operations Research   Check publisher's open access policy
ISSN 0254-5330
1572-9338
Publication date 2011-09
Year available 2009
Sub-type Article (original research)
DOI 10.1007/s10479-009-0611-7
Volume 189
Issue 1
Start page 357
End page 388
Total pages 32
Place of publication United States
Publisher Springer New York LLC
Collection year 2012
Language eng
Subject C1
970101 Expanding Knowledge in the Mathematical Sciences
080110 Simulation and Modelling
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.
Keyword Cross-entropy
Rare events
Importance sampling
State dependence
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
2010 Higher Education Research Data Collection
 
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Created: Tue, 09 Feb 2010, 16:19:44 EST by Kay Mackie on behalf of School of Mathematics & Physics