Efficiency of Monte Carlo computations in very high dimensional spaces

István Deák ()

Central European Journal of Operations Research, 2011, vol. 19, issue 2, 177-189

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

Keywords: Multidimensional normal distribution; Monte Carlo methods; Probabilities of convex sets; Efficiency of estimators; Comparison of performances (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/s10100-010-0166-3

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