A0167
Title: A stratified $L_2$-discrepancy with application to space-filling designs
Authors: Ye Tian - Beijing University of Posts and Telecommunications (China) [presenting]
Hongquan Xu - University of California Los Angeles (United States)
Abstract: Space-filling designs are widely used in computer experiments. A stratified L2-discrepancy is proposed to evaluate the uniformity of a design when the design domain is stratified into various subregions. Weights are used to adjust preferences for uniformity over subregions in each stratification. The stratified L2-discrepancy is easy to compute, satisfies a Koksma-Hlawka-type inequality, and overcomes the curse of dimensionality that exists for other discrepancies. It is applicable to a broad class of designs and covers several minimum aberration-type criteria as special cases. Strong orthogonal arrays of maximum strength are shown to have low stratified L2-discrepancies, and thus are suitable for computer experiments. In addition, a lower bound is developed for the stratified L2-discrepancy, and a construction method is provided for designs that achieve the lower bound. A general version of the stratified L2-discrepancy is further introduced for evaluating designs with flexible stratification properties.