A new kid on the block: The stratification pattern for space‐filling, with dimension by weight tables

Abstract

Designs for computer experiments in quantitative factors use columns with many levels. Filling the experimental space is their most important property, and there are many criteria that assess aspects of space‐filling. Recently, Tian and Xu proposed a stratification pattern for assessing the stratification‐related space‐filling properties of designs for quantitative experimental variables whose number of levels is a power of a – usually small – integer. Such designs have been named GSOAs, in generalization of the earlier proposal of strong – or stratum – orthogonal arrays (SOAs). Latin hypercube designs (LHDs) with a suitable number of levels are special cases of GSOAs. Tian and Xu proposed to use the stratification pattern as a means to ranking (G)SOAs. They reported a small simulation study in which arrays that fared well in that ranking performed well in predicting an unknown function. Shi and Xu refined the criterion and also demonstrated success of a design that fares well on their refined criterion. This paper explains the ideas behind the stratification pattern and the related ranking criteria. A practical example and several toy examples aid the illustration. The stratification pattern can be calculated using the R package SOAs, which does not only provide the pattern itself but also provides more detail in a dimension by weight table, in the spirit of the refinement by Shi and Xu.