Title: Minimum aberration-type criterion and stratification pattern enumerator for selecting space-filling designs

 

Speaker: Hongquan Xu, Department of Statistics and Data Science, University of California, Los Angeles

 

Abstract:  Space-filling designs are widely used in computer experiments. Inspired by the celebrated minimum aberration criterion for fractional factorial designs, we propose a minimum aberration-type criterion 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 through 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, we introduce the concept of stratification pattern enumerator and show 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,  we establish a lower bound  for the stratification pattern enumerator and present construction methods for designs that achieve the lower bound using multiplication tables over Galois fields. The constructed designs have good space-filling properties in low-dimensional projections and are robust under various criteria. 

 

References: 

Tian, Y. and Xu, H.  (2022). A Minimum Aberration-Type Criterion for Selecting Space-Filling Designs. Biometrika,109(2), 489-501.

Tian, Y. and Xu, H. (2024). Stratification Pattern Enumerator and its Applications. Journal of the Royal Statistical Society Series B: Statistical Methodology, 86(2), 364-385.