Accelerating Bayesian Variable Selection and Shrinkage Through Orthogonal Data Augmentation

• Activity Number: 229
• Type: Invited
• Date/Time: Monday, August 10, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Merlise Clyde* and Michael Lindon
• Companies: Duke University and Duke University
• Keywords: Model Selection ; Horseshoe Prior ; Generalized Double Pareto ; EM ; SNPs

Abstract

Bayesian variable selection involves a computationally NP-hard optimization problem to search over the space of possible candidate models. The "Two Group" prior distribution for coefficients that is the basis of the approach involves a mixture of a point mass at zero with a continuos distribution. "One Group" shrinkage priors such as the Horseshoe and Generalized Double Pareto, that involve only a continuous component have been shown to achieve near optimal rates, while avoiding the computational complexity of the two group solution. Through orthogonal data augmentation (ODA) the computational complexity of the variable selection problem can be reduced to order p, the number of predictor variables, which is of the same order of magnitude as the one group solutions. While full posterior inference may still be the ideal, we show how ODA can be used to accelerate finding modal estimates using EM or variational methods under either the one group or two group priors when the dimensionality precludes full posterior inference. We illustrate the methods to an application with fine-scale sequencing data in ovarian cancer.