Scale mixtures of Normals with Rayleigh priors in Tobit quantile regression

This study introduces a new hierarchical formulation of the Bayesian Lasso by incorporating the Scale Mixture of Normals mixing with Rayleigh (BSCNRMIXING prior) into the Tobit Quantile Regression (Tobit Q Regression) framework. The BSCNRMIXING prior is proposed as a promising alternative to the widely used Scale Mixture of Normals mixing with Rayleigh (BSCNRMIXING prior), providing enhanced effectiveness in achieving simultaneous coefficient estimation and variable selection within the Bayesian Lasso paradigm. For Bayesian inference, Gibbs sampling schemes are derived for the full conditional posterior distributions. The proposed methodology is rigorously examined through comprehensive simulation experiments and an application to real data, with comparative analyses against established approaches, thereby highlighting its efficiency, stability, and robustness.