Variable Selection Through Penalized Credible Regions Based on Optimal Dirichlet-Laplace Shrinkage Priors

• Activity Number: 244
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Yan Zhang* and Howard Bondell
• Companies: North Carolina State University and North Carolina State University
• Keywords: Dirichlet-Laplace ; Credible Region ; Variable Selection ; Posterior Consistency ; Concentration ; Bayesian

Abstract

In this paper, we propose a variable selection method combining Dirichlet-Laplace (DL) prior and joint credible interval method as proposed in Bondell and Reich(2012). First, DL prior assumption is made for the full model parameters. As the distribution of the posterior samples could be approximated with normal distribution, joint credible interval algorithm based on normal prior as described in Bondell and Reich (2012) could still be implemented. MCMC runs yield the posterior sample mean and covariance, which would then be plugged into the joint credible interval computing algorithm, to select important variables. Numerical results show that the proposed approach outperforms the original method in Bondell and Reich (2012). We obtain the consistency property for joint credible interval method with normal prior when p = o(n), not limiting to p fixed. We also show that under some mild simple conditions as Armagan et al. (2013a), the posterior distribution would have good concentration within the neighborhoods of the true parameter.