Recent Advances In Randomized Quasi-Monte Carlo Methods
| Citations: | 50 - 11 self |
BibTeX
@MISC{L'Ecuyer_recentadvances,
author = {Pierre L'Ecuyer and Christiane Lemieux},
title = {Recent Advances In Randomized Quasi-Monte Carlo Methods},
year = {}
}
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Abstract
We survey some of the recent developments on quasi-Monte Carlo (QMC) methods, which, in their basic form, are a deterministic counterpart to the Monte Carlo (MC) method. Our main focus is the applicability of these methods to practical problems that involve the estimation of a high-dimensional integral. We review several QMC constructions and dierent randomizations that have been proposed to provide unbiased estimators and for error estimation. Randomizing QMC methods allows us to view them as variance reduction techniques. New and old results on this topic are used to explain how these methods can improve over the MC method in practice. We also discuss how this methodology can be coupled with clever transformations of the integrand in order to reduce the variance further. Additional topics included in this survey are the description of gures of merit used to measure the quality of the constructions underlying these methods, and other related techniques for multidimensional integration. 1 2 1.
