A new Gibbs sampler for Bayesian lasso

Abstract

Lasso regression, a special case of Bridge regression of a penalty function with q = 1, is considered from a Bayesian perspective. Park and Casella (2008) introduced the Bayesian lasso regression, using a conditional Laplace prior distribution represented as a scale mixture of normals with an exponential mixing distribution. Recently, Mallick and Yi (2014) provided a new version of Bayesian lasso regression approach by using a scale mixture of uniform representation of the Laplace distribution with a particular gamma mixing density. In this paper, we propose a new Bayesian lasso regression method by using a scale mixture of truncated normal representation of the Laplace density with exponential mixing densities. The method is illustrated via simulation examples and two real data sets. Results show that the proposed method performs very well. An extension to general models is also discussed.