A Bayesian approach is proposed for coefficient estimation in the Tobit quantile regression model. The
proposed approach is based on placing a g-prior distribution depends on the quantile level on the regression
coefficients. The prior is generalized by introducing a ridge parameter to address important challenges
that may arise with censored data, such as multicollinearity and overfitting problems. Then, a stochastic
search variable selection approach is proposed for Tobit quantile regression model based on g-prior. An
expression for the hyperparameter g is proposed to calibrate the modified g-prior with a ridge parameter to
the corresponding g-prior. Some possible extensions of the proposed approach are discussed, including the
continuous and binary responses in quantile regression. The methods are illustrated using several simulation
studies and a microarray study. The simulation studies and the microarray study indicate that the proposed
approach performs well
