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Abstract:
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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. This paper introduces the orthant normal distribution in a general form and shows 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.
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