Space-filling designs with a Dirichlet distribution for mixture experiments

Astrid Jourdan (1, 2)

1 CY - CY Cergy Paris Université
2 ETIS - UMR 8051 - Equipes Traitement de l'Information et Systèmes

Uniform designs are widely used for experiments with mixtures. The uniformity of the design points is usually evaluated with a discrepancy criterion. In this paper, we propose a new criterion to measure the deviation between the design point distribution and a Dirichlet distribution. The support of the Dirichlet distribution, defined by the set of d-dimensional vectors whose entries are real numbers in the interval [0,1] such that the sum of the coordinates is equal to 1, is suitable for mixture experiments. Depending on its parameters, the Dirichlet distribution allows symmetric or asymmetric, uniform or more concentrated point distribution. The difference between the empirical and the target distributions is evaluated with the Kullback-Leibler divergence. We use two methods to estimate the divergence: the plug-in estimate and the nearest-neighbor estimate. The resulting two criteria are used to build space-filling designs for mixture experiments. They are also compared with two existing criteria in the case of uniform designs.

Mots clés: Space-filling design; mixture experiments; Kullback-leibler divergence; nearest neighbor density estimation; kernel density estimation.

Domaines: Statistiques [math.ST]

Astrid Jourdan. Space-filling designs with a Dirichlet distribution for mixture experiments. 2022. ⟨hal-03418561v2⟩