Scalable Bayesian Variable Selection Using Non-Local Prior Densities in Ultrahigh-Dimensional Settings

• Activity Number: 305
• Type: Topic Contributed
• Date/Time: Tuesday, August 11, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Minsuk Shin* and Anirban Bhattacharya and Valen E. Johnson
• Companies: Texas A&M University and Texas A&M University and Texas A&M University
• Keywords: bayesian variable selection ; high dimensional data ; non-local priors ; L_0 penalized likelihood methods ; scalable algorithms

Abstract

We propose a new class of prior densities for Bayesian model selection, and show that the resulting selection procedure is consistent for linear models even when the number of covariates p increases exponentially with the sample size n, provided that certain regularity constraints are satisfied. We also demonstrate that the non-local prior densities inherent to our selection procedure impose fully adaptive penalties on regression parameters, distinguishing our model selection procedure from existing L_0 penalized likelihood methods. To implement this framework, we propose a scalable algorithm called Simplified Shotgun Stochastic Search with Screening (S5) that efficiently explores high-dimensional model spaces. Compared to standard MCMC algorithms, we demonstrate that S5 can dramatically speed the rate at Bayesian model selection procedures identify high posterior probability models.