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Efficiency of Monte Carlo computations in very high dimensional spaces

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  • István Deák

Abstract

A standard measure for comparing different Monte Carlo estimators is the efficiency, which generally thought to be declining with increasing the number of dimensions. Here we give some numerical examples, ranging from one-hundred to one-thousand dimensional integration problems, that contradict this belief. Monte Carlo integrations carried out in one-thousand dimensional spaces is the other nontrivial result reported here. The examples concern the computation of the probabilities of convex sets (polyhedra and hyperellipsoids) in case of multidimensional normal probabilities. Copyright Springer-Verlag 2011

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  • István Deák, 2011. "Efficiency of Monte Carlo computations in very high dimensional spaces," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 19(2), pages 177-189, June.
    • Handle: RePEc:spr:cejnor:v:19:y:2011:i:2:p:177-189
    DOI: 10.1007/s10100-010-0166-3
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    References listed on IDEAS

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    1. Breslaw, Jon A, 1994. "Evaluation of Multivariate Normal Probability Integrals Using a Low Variance Simulator," The Review of Economics and Statistics, MIT Press, vol. 76(4), pages 673-682, November.
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