Title: Dependence priors for Bayesian regularized regression
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. The orthant normal distribution is introduced in a general form and it is shown how it can be used to structure prior dependence in Bayesian regression models that have connections to penalized optimization procedures. An L1-regularized version of Zellner's $g$ prior is introduced as a special case, creating a new link between the literature on penalized optimization and an important class of regression priors.