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Some Applications of Quasi-Monte Carlo Methods in Statistics

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Monte Carlo and Quasi-Monte Carlo Methods 2000

Abstract

Most applications of quasi-Monte Carlo methods in numerical analysis are in evaluating high dimensional integrals. However, many problems in statistics, that are not obvious integration problems, need low-discrepancy sequences/sets that can be generated by Quasi-Monte Carlo methods. In this paper we review some applications of low-discrepancy sequences/sets in statistical inference, Bayesian statistics, geometric probability and experimental design. Furthermore, measures of uniformity can be regarded as an important criterion in statistical experimental design. We also review various applications of uniformity in factorial design, block design and others.

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  1. Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China

    Kai-Tai Fang

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  1. Kai-Tai Fang
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  1. Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong SAR, China

    Kai-Tai Fang  & Fred J. Hickernell  & 

  2. Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore, 117543, Republic of Singapore

    Harald Niederreiter

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Fang, KT. (2002). Some Applications of Quasi-Monte Carlo Methods in Statistics. In: Fang, KT., Niederreiter, H., Hickernell, F.J. (eds) Monte Carlo and Quasi-Monte Carlo Methods 2000. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56046-0_2

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  • DOI: https://doi.org/10.1007/978-3-642-56046-0_2

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