Bayesian Generalized Horseshoe Estimation of Generalized Linear Models

Abstract

Bayesian global-local shrinkage estimation with the generalized horseshoe prior represents the state-of-the-art for Gaussian regression models. The extension to non-Gaussian data, such as binary or Student-t regression, is usually done by exploiting a scale-mixture-of-normals approach. However, many standard distributions, such as the gamma and the Poisson, do not admit such a representation. We contribute two extensions to global-local shrinkage methodology. The first is an adaption of recent auxiliary gradient based-sampling schemes to the global-local shrinkage framework, which yields simple algorithms for sampling from generalized linear models. We also introduce two new samplers for the..