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Stratified Monte Carlo Integration

1 Département de Mathématiques
USJ - Université Saint-Joseph de Beyrouth
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

https://hal.univ-grenoble-alpes.fr/hal-00950118
Contributeur : Christian Lecot <>
Soumis le : jeudi 20 février 2014 - 18:50:31
Dernière modification le : vendredi 6 novembre 2020 - 03:29:02

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• HAL Id : hal-00950118, version 1

Citation

Rami El Haddad, Fakhereddine R., Christian Lécot. Stratified Monte Carlo Integration. Eighth IMACS Seminar on Monte Carlo Methods, Aug 2011, Borovets, Bulgaria. pp.105-113. ⟨hal-00950118⟩

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