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Modeling Uncertainty pp 419–474Cite as

Recent Advances in Randomized Quasi-Monte Carlo Methods

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Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 46))

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 different 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 figures of merit used to measure the quality of the constructions underlying these methods, and other related techniques for multidimensional integration.

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Authors and Affiliations

  1. Département d’Informatique et de Recherche Opérationnelle, Université de Montréal, C.P. 6128, Succ. Centre-Ville, Montréal, H3C 3J7, Canada

    Pierre L’Ecuyer

  2. Department of Mathematics and Statistics, University of Calgary, 2500 University Drive N.W., Calgary, T2N 1N4, Canada

    Christiane Lemieux

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  1. Pierre L’Ecuyer
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Editors and Affiliations

  1. University of Arizona, USA

    Moshe Dror  & Ferenc Szidarovszky  & 

  2. Université de Montréal, France

    Pierre L’Ecuyer

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© 2002 Springer Science + Business Media, Inc.

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L’Ecuyer, P., Lemieux, C. (2002). Recent Advances in Randomized Quasi-Monte Carlo Methods. In: Dror, M., L’Ecuyer, P., Szidarovszky, F. (eds) Modeling Uncertainty. International Series in Operations Research & Management Science, vol 46. Springer, New York, NY. https://doi.org/10.1007/0-306-48102-2_20

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