嘉宾：张彦 博士(北卡州立)

题目：Bayesian Penalized Credible Region Variable Selection and Global-Local Shrinkage Priors

时间：2015年12月18日上午8:15-9:15

地点：管理科研大楼912会议室

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 when p = o(n). 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 R2 and a prespecified target distribution. Third, I propose a new class of R2 -induced Dirichlet Decomposition (R2- D2) priors. Such prior is induced by a Beta prior on R2 , 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. The R2-D2 prior also enjoys computational tractability with straightforward Gibbs samplers. Posterior consistency of the R2-D2 prior is also shown.

 

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