Bayesian extensions on Lasso and adaptive Lasso Tobit regressions

Abstract

Since lasso method launched, a lot of applications and extensions were run on it which made it to become deeply widely used in various discipline. In this paper, we proposed the Scale Mixture of Normals mixing with Rayleigh (SMNR) distribution on their variances to represent the double exponential distribution. Hierarchical model formula have derived with Gibbs sampler for SMNR. The proposed models; Bayesian Tobit Adaptive Lasso (BTAL) and Bayesian Tobit Lasso (BTL) models are illustrated using simulation example and a real data example through the prediction accuracy using the estimated relative efficiency with different sample. This is the first work that discussed regularization regression models under SMNR.