Bayesian Robust Regression with the Horseshoe+ Estimator

The horseshoe+ estimator for Gaussian linear regression models is a novel extension of the horseshoe estimator that enjoys many favourable theoretical properties. We develop the first efficient Gibbs sampling algorithm for the horseshoe+ estimator for linear and logistic regression models. Importantly, our sampling algorithm incorporates robust data models that naturally handle non-Gaussian data and are less sensitive to outliers. The resulting software implementation provides a powerful, flexible and robust tool for building prediction and classification models from potentially high-dimensional data and represents the state-of-the-art in Bayesian machine learning techniques.