统计与管理学院2015年学术报告第58期
【主 题】Bayesian Penalized Credible Region Variable Selection and Global-Local Shrinkage Priors
【报告人】张彦
Ph.D. student, North Carolina State University
【时 间】 2015年12月24日（星期四）13:30－14:30
【地 点】 上海财经大学统计与管理学院大楼1208室
【语 言】 英文
【摘 要】More recently, improvements in the use of global-local shrinkage priors have been made for high-dimensional applications. The method of Bayesian variable selection via penalized credible regions separates model fitting and variable selection. Although the approach was successful, it depended on the use of conjugate normal priors. In this talk, first, I will talk about the method of incorporating global-local priors into the credible region selection framework. The Dirichlet-Laplace prior is adapted to linear regression. Variable selection consistency together with posterior consistency is got. Second, I introduce a new method to tune hyperparameters in prior distributions. The hyperparameters are chosen to minimize a discrepancy between the induced distribution on R-square and a prespecified target distribution. Third, I propose a new class of R-square induced Dirichlet Decomposition (R2-D2) priors. Such prior is induced by a Beta prior on R-square, and then the total prior variance of the regression coefficients is decomposed through a Dirichlet prior. We demonstrate theoretically and empirically the advantages of the R2-D2 prior, over a number of common global-local shrinkage priors, including the Horseshoe, Horseshoe+, and Dirichlet-Laplace priors.
This is joint work with Professors Howard D. Bondell and Brian J. Reich.
