Some Applications of Quasi-Monte Carlo Methods in Statistics

Kai Tai Fang

doi:10.1007/978-3-642-56046-0_2

Some Applications of Quasi-Monte Carlo Methods in Statistics

Kai Tai Fang^*

^*Corresponding author for this work

Research output: Chapter in book/report/conference proceeding › Conference proceeding

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.

Original language	English
Title of host publication	Monte Carlo and Quasi-Monte Carlo Methods 2000
Subtitle of host publication	Proceedings of a Conference held at Hong Kong Baptist University, Hong Kong SAR, China, November 27 – December 1, 2000
Editors	Kai Tai Fang, Harald Niederreiter, Fred J. Hickernell
Publisher	Springer Berlin Heidelberg
Pages	10–26
Number of pages	17
Edition	1st
ISBN (Electronic)	9783642560460
ISBN (Print)	9783540427186
DOIs	https://doi.org/10.1007/978-3-642-56046-0_2
Publication status	Published - 22 Jan 2002
Externally published	Yes
Event	4th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCMQC 2000 - Hong Kong Baptist University, Hong Kong Duration: 27 Nov 2000 → 1 Dec 2000 https://www.math.hkbu.edu.hk/mcqmc/MCQMC2000.html (Link to conference website) https://link.springer.com/book/10.1007/978-3-642-56046-0 (Link to conference proceedings)

Conference

Conference	4th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCMQC 2000
Country/Territory	Hong Kong
Period	27/11/00 → 1/12/00
Internet address	https://www.math.hkbu.edu.hk/mcqmc/MCQMC2000.html (Link to conference website) https://link.springer.com/book/10.1007/978-3-642-56046-0 (Link to conference proceedings)

User-Defined Keywords

Monte Carlo
Fractional Factorial Design
Orthogonal Design
Star Discrepancy
Hadamard Matrice

Access to Document

10.1007/978-3-642-56046-0_2

Cite this

Fang, K. T. (2002). Some Applications of Quasi-Monte Carlo Methods in Statistics. In K. T. Fang, H. Niederreiter, & F. J. Hickernell (Eds.), Monte Carlo and Quasi-Monte Carlo Methods 2000: Proceedings of a Conference held at Hong Kong Baptist University, Hong Kong SAR, China, November 27 – December 1, 2000 (1st ed., pp. 10–26). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-56046-0_2

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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.",

keywords = "Monte Carlo, Fractional Factorial Design, Orthogonal Design, Star Discrepancy, Hadamard Matrice",

author = "Fang, {Kai Tai}",

note = "Funding information: This work was partially supported by the Hong Kong RGC Grant HKBU RC/98-99/Gen-370. The author is grateful to Harald Niederreiter and Fred J. Hickernell for their valuable comments and encouragement and to the Referee for valuable comments. Publisher copyright: {\textcopyright} 2002 Springer-Verlag Berlin Heidelberg; 4th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCMQC 2000 ; Conference date: 27-11-2000 Through 01-12-2000",

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Fang, KT 2002, Some Applications of Quasi-Monte Carlo Methods in Statistics. in KT Fang, H Niederreiter & FJ Hickernell (eds), Monte Carlo and Quasi-Monte Carlo Methods 2000: Proceedings of a Conference held at Hong Kong Baptist University, Hong Kong SAR, China, November 27 – December 1, 2000. 1st edn, Springer Berlin Heidelberg, pp. 10–26, 4th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCMQC 2000, Hong Kong, 27/11/00. https://doi.org/10.1007/978-3-642-56046-0_2

Some Applications of Quasi-Monte Carlo Methods in Statistics. / Fang, Kai Tai.
Monte Carlo and Quasi-Monte Carlo Methods 2000: Proceedings of a Conference held at Hong Kong Baptist University, Hong Kong SAR, China, November 27 – December 1, 2000. ed. / Kai Tai Fang; Harald Niederreiter; Fred J. Hickernell. 1st. ed. Springer Berlin Heidelberg, 2002. p. 10–26.

Research output: Chapter in book/report/conference proceeding › Conference proceeding

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PY - 2002/1/22

Y1 - 2002/1/22

N2 - 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.

AB - 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.

KW - Monte Carlo

KW - Fractional Factorial Design

KW - Orthogonal Design

KW - Star Discrepancy

KW - Hadamard Matrice

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Fang KT. Some Applications of Quasi-Monte Carlo Methods in Statistics. In Fang KT, Niederreiter H, Hickernell FJ, editors, Monte Carlo and Quasi-Monte Carlo Methods 2000: Proceedings of a Conference held at Hong Kong Baptist University, Hong Kong SAR, China, November 27 – December 1, 2000. 1st ed. Springer Berlin Heidelberg. 2002. p. 10–26 doi: 10.1007/978-3-642-56046-0_2

Some Applications of Quasi-Monte Carlo Methods in Statistics

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Conference

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