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Hot New Directions for Quasi-Monte Carlo Research in Step with Applications

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Monte Carlo and Quasi-Monte Carlo Methods (MCQMC 2016)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 241))

Abstract

This article provides an overview of some interfaces between the theory of quasi-Monte Carlo (QMC) methods and applications. We summarize three QMC theoretical settings: first order QMC methods in the unit cube \([0,1]^s\) and in \({\mathbb {R}}^s\), and higher order QMC methods in the unit cube. One important feature is that their error bounds can be independent of the dimension s under appropriate conditions on the function spaces. Another important feature is that good parameters for these QMC methods can be obtained by fast efficient algorithms even when s is large. We outline three different applications and explain how they can tap into the different QMC theory. We also discuss three cost saving strategies that can be combined with QMC in these applications. Many of these recent QMC theory and methods are developed not in isolation, but in close connection with applications.

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Acknowledgements

The authors acknowledge the financial supports from the Australian Research Council (FT130100655 and DP150101770) and the KU Leuven research fund (OT:3E130287 and C3:3E150478).

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Authors and Affiliations

  1. School of Mathematics and Statistics, University of New South Wales, Sydney, NSW, 2052, Australia

    Frances Y. Kuo

  2. Department of Computer Science, KU Leuven, Celestijnenlaan 200A, 3001, Leuven, Belgium

    Dirk Nuyens

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  1. Frances Y. Kuo
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Correspondence to Frances Y. Kuo .

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Editors and Affiliations

  1. Department of Statistics, Stanford University, Stanford, California, USA

    Art B. Owen

  2. Department of Management Science and Engineering, Stanford University, Stanford, California, USA

    Peter W. Glynn

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Kuo, F.Y., Nuyens, D. (2018). Hot New Directions for Quasi-Monte Carlo Research in Step with Applications. In: Owen, A., Glynn, P. (eds) Monte Carlo and Quasi-Monte Carlo Methods. MCQMC 2016. Springer Proceedings in Mathematics & Statistics, vol 241. Springer, Cham. https://doi.org/10.1007/978-3-319-91436-7_6

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