A0160
Title: Minimum aberration-type criterion and stratification pattern enumerator for selecting space-filling designs
Authors: Hongquan Xu - University of California Los Angeles (United States) [presenting]
Abstract: Space-filling designs are widely used in computer experiments. Inspired by the celebrated minimum aberration criterion for fractional factorial designs, a minimum aberration-type criterion is proposed for assessing the space-filling properties of a broad class of designs, including Latin hypercube designs, orthogonal arrays, and strong orthogonal arrays. The new minimum aberration-type criterion covers the minimum aberration criterion and various generalizations as special cases. The generality of the new criterion comes with a huge computational cost. The fast computation of the (generalized) minimum aberration criterion is facilitated by the famous MacWilliams identities, a fundamental result in coding theory. There are no parallel results to handle complex design problems with stratifications. To address the computational issue, the concept of stratification pattern enumerator is introduced, and it is shown that the stratification pattern enumerator is a linear combination of the space-filling pattern. The stratification pattern enumerator is more general than the MacWilliams identities, and it can be used to compute the space-filling or stratification pattern in quadratic times instead of exponential times by definition. In addition, a lower bound for the stratification pattern enumerator is established, and construction methods are presented for designs that achieve the lower bound using multiplication tables over Galois fields.
