Stratified Monte Carlo Integration

Abstract : We analyze a Monte Carlo method using stratified sampling for approximate integration. We focus on integration of non-smooth functions: we consider the indicator function of a Jordan-measurable subset of the $s$-dimensional unit cube $I^s := [0,1)^s$. We prove a bound for the variance and show an improved convergence rate (compared to plain Monte Carlo). When the boundary of the subset is defined by a function on $I^{s-1}$, the variance is estimated by means of the variation of the function. The tightness of the previous bounds is assessed through numerical experiments in dimensions $s=2,3$ and $4$, where we compute sample variances.
Type de document :
Communication dans un congrès
K.K. Sabelfeld, I. Dimov. Eighth IMACS Seminar on Monte Carlo Methods, Aug 2011, Borovets, Bulgaria. De Gruyter, pp.105-113, 2013
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http://hal.univ-grenoble-alpes.fr/hal-00950118
Contributeur : Christian Lecot <>
Soumis le : jeudi 20 février 2014 - 18:50:31
Dernière modification le : jeudi 11 janvier 2018 - 06:12:26

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  • HAL Id : hal-00950118, version 1

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Rami El Haddad, Fakhereddine R., Christian Lécot. Stratified Monte Carlo Integration. K.K. Sabelfeld, I. Dimov. Eighth IMACS Seminar on Monte Carlo Methods, Aug 2011, Borovets, Bulgaria. De Gruyter, pp.105-113, 2013. 〈hal-00950118〉

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