Sparsity via new Bayesian Lasso

Abstract

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.