Title: Computational aspects of L1-regularized $g$ priors
Authors: Christopher Hans - The Ohio State University (United States) [presenting]
Abstract: Many regularization priors for Bayesian regression assume the regression coefficients are a priori independent. In particular this is the case for Bayesian treatments of the lasso and the elastic net. While independence may be reasonable in some data-analytic settings, having the ability to incorporate dependence in these prior distributions would allow for greater modeling flexibility. L1-regularized g priors are one such approach to incorporating dependence and represent a special case of a general ``orthant normal'' prior. We investigate properties of these L1-regularized g priors and discuss efficient posterior computation. Evaluating the moment generating function of the L1-norm of a multivariate normal random vector plays a critical role in computation. We introduce bounds for this quantity and investigate several computational approaches for estimation of it. The results are applied to the problem of model comparison and variable selection in the L1-regularized g prior setting.