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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

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

Regression models are important tools in estimating the effect relationships between the dependent variable and a set of independent variables. To estimate the parameters of the studied model, there are various estimation methods Bayesian and non-Bayesian are will used . The obesity affected with many independent variables some these variables have direct effecting and non- direct, therefor choosing optimal variables that effecting in our model considered give us high explanatory power for the studied phenomenon, in this variable there are subset variables effecting on obesity via many different quantiles level