时间：2018年6月27日 下午2:00-4:00
地点：明德主楼1016会议室
题目: D-optimal Designs for Multinomial Logistic Models
摘要： Design of experiment with categorical responses is becoming increasingly popular in a rich variety of scientific disciplines. When the response has three or more categories, the models used in the literature are special cases of multinomial logistic models, including baseline-category, cumulative, adjacent-categories, and continuation-ratio logit models. We derive the corresponding Fisher information matrices in three different forms to facilitate their calculations, the determination of conditions for their positive definiteness, and the search for D-optimal designs, respectively. We conclude that, unlike the designs for binary responses, a feasible design for a multinomial logistic model may contain less experimental settings than parameters, which is of practical significance. We also conclude that even for a minimally supported design, a uniform allocation, which is typically used in practice, is not optimal in general for a multinomial logistic model. We develop efficient algorithms for searching D-optimal designs. Using examples based on real experiments, we show that the efficiency of an experiment can be significantly improved if our designs are adopted.
简介：杨杰，美国伊利诺伊大学芝加哥分校数学、统计和计算机科学系副教授，统计实验室主任。2001年获南开大学金融数学博士学位，2006年获美国芝加哥大学统计系博士学位；多年从事统计学、金融数学、生物信息学、大数据统计分析的教学科研工作；研究成果包括生物大分子快速分类方法、 高维数据统计分类方法、 最优实验设计理论及应用、金融衍生品实时定价方法和大数据抽样分析方法等；已在国际知名学术期刊发表论文几十篇，应邀在几十所国内外知名大学做过学术报告。