报告题目：:A Bayesian method for non-sparse high-dimensional linear models

报告人：吴月华

邀请人：胡雪梅

报告时间：6月2日，上午10：00

报告地点：启智楼80602

参加人员：学院师生代表

报告摘要：In high-dimensional linear regression, the common assumption of sparsity in regression coefficients often does not reflect real-world scenarios where most, if not all, coefficients are non-zero. However, when the majority of coefficients are indeed non-zero, methods designed for sparse models can introduce considerable bias. In this talk, we introduce a Bayesian method for non-sparse high-dimensional linear models. We propose an approach named Bayesian Grouping-Gibbs Sampling (BGGS), which uses a grouping strategy to partition the regression coefficients into distinct subsets, facilitating rapid sampling in high-dimensional space. The grouping number can be determined by using the “Elbow plot”, which operates efficiently and is robust against the initial value. Our theoretical analysis establishes consistency in model selection and parameter estimation, along with bounds for prediction error, under certain regularity conditions. To further validate its efficacy, we present results from

报告人简介：吴月华，加拿大约克大学数学与统计系教授。她师从世界著名统计学家 C. R. Rao，于 1989 年获得美国匹兹堡大学统计学博士学位。目前，她从事高维数据分析、模型选择、变点分析、时空建模、环境统计、统计金融和贝叶斯方法等多领域研究，是国际统计学会的当选会员。她在 Proceedings of the National Academy of Sciences, USA、Biometrika、Journal of Economics 等期刊上发表了 150 余篇学术论文，并长期承担加拿大国家自然科学基金科研项目。此外，她目前担任 Entropy Section Board Member，Entropy 特刊“用于对高维和复杂数据进行建模的统计方法：第三期”的客座编辑，以及 Springer Nature 系列丛书“数学奇迹：本着 CR Rao 精神的文本和专著”编辑委员会副主编。