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A comparison of cross-entropy and variance minimization strategies

Part of: Probabilistic methods, simulation and stochastic differential equations

Published online by Cambridge University Press:  14 July 2016

Joshua C. C. Chan ,
Peter W. Glynn  and
Dirk P. Kroese
Joshua C. C. Chan
Affiliation:
Australian National University, Research School of Economics, Australian National University, Canberra, ACT 0200, Australia
Peter W. Glynn
Affiliation:
Stanford University, Department of Management Science and Engineering, Huang Engineering Center, Stanford University, Stanford University, 475 Via Ortega, Stanford, CA 94305-4121, USA
Dirk P. Kroese
Affiliation:
University of Queensland, Department of Mathematics, University of Queensland, St Lucia, Brisbane, QLD 4072, Australia. Email address: kroese@maths.uq.edu.au
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Abstract

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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.

Keywords

Variance minimizationcross entropyimportance samplingrare-event simulationlikelihood ratio degeneracy

MSC classification

Primary: 65C05: Monte Carlo methods
Secondary: 65C60: Computational problems in statistics
Type
Part 4. Simulation
Information
Journal of Applied Probability , Volume 48 , Issue A: New Frontiers in Applied Probability (Journal of Applied Probability Special Volume 48A) , August 2011 , pp. 183 - 194
Copyright
Copyright © Applied Probability Trust 2011 

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