Bayesian Inference in High-Dimensional Linear Regression Using an Empirical Correlation-Adaptive Prior

• Activity Number: 256 - Contributed Poster Presentations: Section on Bayesian Statistical Science
• Type: Contributed
• Date/Time: Monday, July 30, 2018 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Chang Liu* and Yue Yang and Howard D Bondell and Ryan Martin
• Companies: North Carolina State University and North Carolina State University and University of Melbourne and North Carolina State University
• Keywords: Bayesian variable selection; Zellner's prior; collinearity; posterior convergence rate; high-dimensional model

Abstract

In this paper, we propose a new empirical Bayesian inference and variable selection method for high-dimensional linear models. The chief novelty is our use of a correlation-adaptive prior that makes use of information in the observed predictor variable matrix to adaptively address high collinearity, determining if parameters associated with correlated predictors should be shrunk together or kept apart. We also investigate asymptotic posterior convergence rate properties for our method. A simplified version of shotgun stochastic search algorithm is employed to implement the variable selection procedure, and the performance of our method is assessed against other existing methods, such as lasso, via simulation studies across different experimental settings and a real-data problem. In both real- and simulated-data examples, our method demonstrates significant advantage compared with the other methods.