Bayesian extensions on Lasso and adaptive Lasso Tobit regressions

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

Bayesian estimation and variables selection for binary composite quantile regression

In this paper, Bayesian hierarchical model proposed to estimate the coefficients of the composite quantile regression model when the response variable is binary. For selecting variables in binary composite quantile regression lasso the adaptive lasso penalty is derived in a Bayesian framework. Simulation study and real data examples are used to examine the performance of the proposed methods compared to the other existing methods. We conclude that the proposed method is comparable

Sparsity via new Bayesian Lasso

Lasso estimate as the posterior mode assuming that the parameter has prior density as double exponential distribution [1]. In this paper, we proposed Scale Mixture of Normals mixing with Rayleigh (SMNR) density on their variances to represent the double exponential distribution. Hierarchical model formulation presented with Gibbs sampler under SMNR as alternative Bayesian analysis of minimization problem of classical lasso. We conducted two simulation examples to explore path solution of the Ridge, Lasso, Bayesian Lasso, and New Bayesian Lasso (R, L, BL, NBL) regression methods through the prediction accuracy using the bias of the estimates with different sample sizes, bias indicates that the lasso regression perform well, followed by the NBL. The Median Mean Absolute Deviations (MMAD) used to compared the perform of the regression methods using real data, MMAD indicates that the proposed method (NBL) perform better than the others