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Comparison of descriptive statistics for multidimensional point sets

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  • Beachkofski Brian

    (AFRL/RZTS, 1950 5th Street, Wright-Patterson AFB, OH 45433, USA. Email: brian.beachkofski@us.af.mil)

Abstract

This work produces a statistical description of several sample-based techniques for numerical integration probabilistic assessment. The sampling techniques include pseudo-random, quasi-random, and centroidal Voronoi tessellation methods. The compared statistics are the star-discrepancy, minimum distance between points, and independence of sample sets. These statistics are selected because they influence the size of confidence intervals generated by repeated analyses. The optimal distance between points for two, three and four dimensions is derived as well as the general form for m dimensions. The results show that for problems with few random variables the complex methods would produce smaller confidence intervals. However, the benefits of more complex techniques are marginalized when there are more random variables.

Suggested Citation

  • Beachkofski Brian, 2009. "Comparison of descriptive statistics for multidimensional point sets," Monte Carlo Methods and Applications, De Gruyter, vol. 15(3), pages 211-228, January.
    • Handle: RePEc:bpj:mcmeap:v:15:y:2009:i:3:p:211-228:n:2
    DOI: 10.1515/MCMA.2009.012
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    References listed on IDEAS

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    1. Romero, Vicente J. & Burkardt, John V. & Gunzburger, Max D. & Peterson, Janet S., 2006. "Comparison of pure and “Latinized†centroidal Voronoi tessellation against various other statistical sampling methods," Reliability Engineering and System Safety, Elsevier, vol. 91(10), pages 1266-1280.
    2. Usabel, Miguel A., 1998. "Applications to risk theory of a Monte Carlo multiple integration method," Insurance: Mathematics and Economics, Elsevier, vol. 23(1), pages 71-83, October.
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