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

François Wahl (1, 2) , Cécile Mercadier (2) , Céline Helbert (3, 2, 4, 5, 6)

1 IFPEN - IFP Energies nouvelles
2 PSPM - Probabilités, statistique, physique mathématique
3 UCBL - Université Claude Bernard Lyon 1
4 ICJ - Institut Camille Jordan
5 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques
6 ECL - École Centrale de Lyon

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 Lp 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.

Mots clés: Minimal distance; Computer experiments; Space-filling design; Maximin; Extreme value theory

Domaines: Informatique [cs]

François Wahl, Cécile Mercadier, Céline Helbert. A standardized distance-based index to assess the quality of space-filling designs. Statistics and Computing, 2017, 27 (2), pp.319 - 329. ⟨10.1007/s11222-015-9624-z⟩. ⟨hal-01804865⟩