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Deterministic construction methods for uniform designs

发布时间:2022-11-17 作者: 浏览次数:
Speaker: 周永道 DateTime: 2022年11月23日(星期三)下午2:00-3:00
Brief Introduction to Speaker:

周永道,男,南开大学统计与数据科学学院教授、博导,中组部青年拔尖人才,天津市创新类领军人才、天津市131创新型人才、南开大学百名青年学科带头人。研究方向为试验设计和数据挖掘。主持过四项国家自然科学基金、一项天津市自然科学基金重点项目及其它多项纵横向项目。曾访问加州大学洛杉矶分校、西蒙菲莎大学、曼彻斯特大学、香港大学等高校。在统计学顶级期刊 JASABiometrika 及中国科学等国内外重要期刊发表学术论文50多篇;合作出版了两本中英文专著和两本统计学专业教材。曾获国家统计局统计科学研究优秀成果奖一等奖。现为中国数学会均匀设计分会秘书长、泛华统计协会永久会员、美国《数学评论》评论员。

 

Place: 腾讯会议:953-488-158
Abstract:Space-filling designs are useful for exploring the relationship between the response and factors, especially when the true model is unknown. The wrap around L2-discrepancy is an important measure of the uniformity, and has often been used as a type of space-filling criterion. However, most obtained designs are generated through stochastic optimization algorithms, and can not achieve the lower bound of the discrepancies and are only nearly uniform. Then deterministic construction methods for uniform designs are desired. We construct uniform designs under the wrap-around L2-discrepancy by generator matrices of linear codes. Several requirements on the generator matrices, such as a necessary and sufficient condition for generating uniform designs, are derived. Based on these, two simple deterministic constructions for uniform designs are given. Some examples illustrate the effectiveness of them. Moreover, the resulting designs can be regarded as a generalization of good lattice point s...