Comparison of descriptive statistics for multidimensional point sets

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

Monte Carlo Methods and Applications, 2009, vol. 15, issue 3, 211-228

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.

Keywords: Latin Hypercube Sampling; Monte Carlo; low-discrepancy; Centroidal Voronoi Tessellation (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1515/MCMA.2009.012

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