A maximum projective stratification criterion for selecting space-filling designs

Abstract

Space-filling designs are commonly used in computer experiments. In this paper, we propose a maximum projective stratification criterion for classifying and ranking space-filling designs. We first introduce a stratification metric, which is proved to be a variance decomposition of the frequency representation of a design. Based on this metric, we define the new criterion to sequentially minimize a projective stratification pattern, that quantifies the stratification property of a design when projected into one up to full dimensions. Numerical results show that, when the space-filling property in cluster of projections with respect to dimensions is paid attention on, our criterion is more rational than existing criteria. We further study the intimate connections between our criterion and existing criteria. The extension of this criterion for a design with prime power levels to general levels are also discussed.