New Scale Mixture for Bayesian Adaptive Lasso Tobit Regression

Abstract

Abbas [1] proposed new hierarchical representation of the adaptive Bayesian lasso model as uniform density , mixing with standard exponential distribution based on a transformation of the mixture of uniform density and a particular gamma distribution formulation provided by Mallick & Yi [2] They consider the new proposed hierarchical formulation model and prior distributions, as well as the full Conditional posterior distributions structural under non conditioning on σ2 which makes the uncertainty, of a unimodal full posterior, Conditioning on σ2 is important, because it guarantees a unimodal full posterior Park and Casella [3]. So, we can conclude that [1] proposed new hierarchical representation utilizing a Non- scale mixture distributions, which needs to deal with this problem . To address this problem we consider new hierarchical representation of the adaptive Bayesian lasso for Tobit model based on scale mixture of Uniform density, mixing with standard exponential distribution.