Developing a Bayesian Technique Employing a Posterior based on mode to Estimate Parameters in Multiple Linear Regression (simulation study)

The process of estimating the parameters of regression is still one of the most important. Despite the large number of papers and studies written on this subject, these studies differ in the techniques followed in the process of estimation, whether they are classic or Bayesian. In this study, we developed a Bayesian technique employing a posterior-based mode to estimate parameters in multiple linear regression. The best multiple linear regression model for the data may be obtained based on the mean squared error after comparing the Bayesian posterior based on mode and the traditional method (ordinary least squares) by combining simulated and real data with a MATLAB program made especially for this purpose. The study finds that, compared to the traditional approach, the Bayesian posterior based on mode approach yields more accurate parameter estimates and In terms of the RMSE statistical criterion, the best results for estimating the multiple linear