A robust Bayesian analysis of variable selection in linear models with spherically symmetric errors

报告题目：A robust Bayesian analysis of variable selection in linear models with spherically symmetric errors

报告人：汪敏 德州大学圣安东尼奥分校教授博导

报告时间：2024年 6 月 13 日16：30-18:30

报告地点：明理楼C302B

报告人简介：

汪敏（Min Wang），美国德州大学圣安东尼奥分校 (University of Texas at San Antonio) 商学院(Carlos Alvarez College of Business)管理科学与统计系教授和应用统计博士项目负责人，博士生导师。2010年5月于美国克莱姆森大学（Clemson University）获得统计硕士学位；2013年5月于克莱姆森大学获得统计博士学位。2013年8月- 2017年12月在美国密歇根理工大学数学科学系工作在2017年8月破格提前提升为副教授并获得终身任期教授资格。现在德州大学圣安东尼奥分校从事教学科研工作。近年来，先后参与和主持了美国自然科学基金委，密歇根交通部，以及美国卫生院的研究课题。在各类同行评议的国际期刊上发表了研究文章100余篇。研究方向：贝叶斯统计；计算统计；统计推断；质量和可靠性工程研究；高维数据分析和统计应用。

报告内容摘要:

Response surface methodology is an effective tool for improving an overall manufacture process where quality requirements are fulfilled. This work proposes a double-robust Bayesian approach that can simultaneously cope with the variable selection, model form uncertainty, and non-normality for quality prediction. Double robust is achieved by specifying the class of spherically symmetric distributions for the errors and accounting for model form uncertainty through Bayesian model averaging. We propose a closed-form marginal posterior distribution of each candidate model, which is not only free of the error distributions (other than spherical symmetry), but also is easily computed in standard software. In addition, a special prior is specified for the model space to maintain the hierarchical relationships among input variables. The proposed Bayesian method has the properties of variable selection consistency and prediction consistency. Numerical results show that the proposed Bayesian method is shown to achieve results superior to those of the existing established methods in terms of prediction and variable selection in linear models under different types of error distributions.

主办单位：理学院、人工智能研究院、非线性动力系统研究所

数理力学研究中心 、科学技术发展研究院