A standardized distance-based index to assess the quality of space-filling designs

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• 作者：François Wahl ; Cécile Mercadier ; Céline Helbert
• 关键词：Minimal distance ; Maximin ; Space ; filling design ; Computer experiments ; Extreme value theory
• 刊名：Statistics and Computing
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：27
• 期：2
• 页码：319-329
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics and Computing/Statistics Programs; Artificial Intelligence (incl. Robotics); Statistical Theory and Methods; Probability and Statistics in Computer Science;
• 出版者：Springer US
• ISSN：1573-1375
• 卷排序：27

文摘

One of the most used criterion for evaluating space-filling design in computer experiments is the minimal distance between pairs of points. The focus of this paper is to propose a normalized quality index that is based on the distribution of the minimal distance when points are drawn independently from the uniform distribution over the unit hypercube. Expressions of this index are explicitly given in terms of polynomials under any \(L_p\) distance. When the size of the design or the dimension of the space is large, approximations relying on extreme value theory are derived. Some illustrations of our index are presented on simulated data and on a real problem.