报告题目: A Stratified L_2-Discrepancy with Application to Space-Filling Designs

报告人：田烨（北京邮电大学特聘副研究员）

报告时间：2024年12月26日 10:00

报告地点：文波楼智慧教室205

摘要: Space-filling designs are widely used in computer experiments. We propose a stratified L_2-discrepancy to evaluate the uniformity of a design when the design domain is stratified into various subregions. Weights are used to adjust preferences for the uniformity over subregions in each stratification. The stratified L_2-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 L_2-discrepancies, and thus are suitable for computer experiments.In addition, we develop a lower bound for the stratified L_2-discrepancy and provide a construction method for designs that achieve the lower bound. We further introduce a general version of the stratified L_2-discrepancy for evaluating designs with flexible stratification properties.

报告人简介: 田烨，特聘副研究员，就职于北京邮电大学理学院数学系，2021年博士毕业于加利福尼亚大学洛杉矶分校统计系。从事试验设计相关研究，研究方向主要包括计算机试验设计、空间填充设计、强正交表、均匀设计、大数据抽样方法与试验设计方法的结合研究等，研究成果包括具有分层性质的空间填充评价准则的提出、最优设计的构建等。曾在Biometrika, Journal of the Royal Statistical Society, Series B (Statistical Methodology)上发表文章。