A1060
Title: Empirical priors inference in sparse high-dimensional generalized linear models
Authors: Yiqi Tang - Colby College (United States) [presenting]
Ryan Martin - North Carolina State University (United States)
Abstract: High-dimensional linear models have been widely studied, but the developments in high-dimensional generalized linear models, or GLMs, have been slower. The focus is on the novel empirical or data-driven prior framework for inference on the coefficient vector and for variable selection in high-dimensional GLM. In this framework, data is used to appropriately center the prior distribution, leading to an empirical Bayes posterior distribution. The proposed posterior distribution is shown to concentrate around the true/sparse coefficient vector at the optimal rate, and conditions under which the posterior can achieve variable selection consistency are provided. Computation of the proposed empirical Bayes posterior is simple and efficient and is shown to perform well in simulations compared to existing methods in terms of estimation and variable selection.
