Studying the Bayesian Generalized Lasso via Simulation

Abstract

In this paper, one of the topics of Bayes' theory was dealt with in estimating the parameters of the multiple linear regression model, as the estimation process in statistical theory is one of the most important and common topics in various scientific fields. This paper dealt with the so-called Safe Bayesian method in estimating the parameters of the multiple linear regression model, as this method is considered a method for solving problems that accompany the misdiagnosis of regression relationships between variables. The misdiagnosis of the regression model for the assumed data leads to inconsistent estimates of the parameters of the regression model under study, which means that these estimates are unhelpful, and therefore the explanatory variables included in the model do not correctly explain the changes in the average of the response variable. The Bayes method was employed in estimating the parameters of the multiple regression model proposed by the researchers Mallick and Yi in 2014 by using the lasso penalty method and assuming that the a priori distribution of the regression parameter is a Laplace distribution that can be represented by mixing the two distributions of Gamma (2,λ) and the Uniform distribution. In this paper, the researcher employed the Bayesian Safe theory on the method that proposed by Mallick and Yi, and an experimental examination was conducted for the behavior of the Lasso penalty method according to the Bayesian Safe theory through several simulation experiments, clearly the proposed method outperformed the other exits methods. This means that there is an important role for the learning parameter in the Bayes method in increasing the probability of obtaining the correct distribution through the role of the learning parameter in studying the behavior of the likelihood distribution.