報(bào)告題目：A robust Bayesian analysis of variable selection in linear models with spherically symmetric errors

報(bào)告人：汪敏 德州大學(xué)圣安東尼奧分校教授博導(dǎo)

報(bào)告時(shí)間：2024年 6 月 13 日16：30-18:30

報(bào)告地點(diǎn)：明理樓C302B

報(bào)告人簡(jiǎn)介：

汪敏（Min Wang），美國(guó)德州大學(xué)圣安東尼奧分校 (University of Texas at San Antonio) 商學(xué)院(Carlos Alvarez College of Business)管理科學(xué)與統(tǒng)計(jì)系教授和應(yīng)用統(tǒng)計(jì)博士項(xiàng)目負(fù)責(zé)人，博士生導(dǎo)師。2010年5月于美國(guó)克萊姆森大學(xué)（Clemson University）獲得統(tǒng)計(jì)碩士學(xué)位；2013年5月于克萊姆森大學(xué)獲得統(tǒng)計(jì)博士學(xué)位。2013年8月- 2017年12月在美國(guó)密歇根理工大學(xué)數(shù)學(xué)科學(xué)系工作在2017年8月破格提前提升為副教授并獲得終身任期教授資格。現(xiàn)在德州大學(xué)圣安東尼奧分校從事教學(xué)科研工作。近年來(lái)，先后參與和主持了美國(guó)自然科學(xué)基金委，密歇根交通部，以及美國(guó)衛(wèi)生院的研究課題。在各類(lèi)同行評(píng)議的國(guó)際期刊上發(fā)表了研究文章100余篇。研究方向：貝葉斯統(tǒng)計(jì)；計(jì)算統(tǒng)計(jì)；統(tǒng)計(jì)推斷；質(zhì)量和可靠性工程研究；高維數(shù)據(jù)分析和統(tǒng)計(jì)應(yīng)用。

報(bào)告內(nèi)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.

主辦單位：理學(xué)院、人工智能研究院、非線(xiàn)性動(dòng)力系統(tǒng)研究所

數(shù)理力學(xué)研究中心 、科學(xué)技術(shù)發(fā)展研究院