High-Dimensional Bayesian Regularised Regression with the BayesReg Package

Abstract

Bayesian penalized regression techniques, such as the Bayesian lasso and the Bayesian horseshoe estimator, have recently received a significant amount of attention in the statistics literature. However, software implementing state-of-the-art Bayesian penalized regression, outside of general purpose Markov chain Monte Carlo platforms such as STAN, is relatively rare. This paper introduces bayesreg, a new toolbox for fitting Bayesian penalized regression models with continuous shrinkage prior densities. The toolbox features Bayesian linear regression with Gaussian or heavy-tailed error models and Bayesian logistic regression with ridge, lasso, horseshoe and horseshoe$+$ estimators. The toolbox is free, open-source and available for use with the MATLAB and R numerical platforms.