Safe Bayesian Quantile Regression

Abstract

In Bayesian estimation of the quantile regression parameters become more accurate estimate if the likelihood function equipped with learning rate parameter (safe Bayesian). Learning rate parameter can be se to solve the problem of overfitting of the estimated model. The amount of the data (likelihood) can be controlled by the learning rate parameter which reflects on the good conclusion that drawn.  Bayesian estimation under the likelihood with leaning rate parameter results the so called learning rate generalized posterior. Choosing the appropriate learning rate parameter is the key idea of this paper, simulation study has conducted based on suggesting that the learning rate parameter follows the multinomial distribution. New Gibbs sampler algorithm has developed beside the quantile regression. Real data analysis has done with the response variable that represents the creatinine in the blood along with some predictor variables. Based on the results of simulation study and real data we have conclude that the proposed model is perform well along with other different regression models.