Bayesian Screening of Covariates in Linear Regression Models Using Correlation Thresholds

In this work, we propose a fast and simple Bayesian method based on simple and partial correlation coefficients to identify covariates which are not supported in terms of the Bayes Factors in normal linear regression models. By this way, when the number of the covariates is large, we can screen out the covariates with negligible effects and reduce the size of the model space in such a way that we can implement traditional Bayesian variable selection methods.We focus on the g-prior implementation where computations are exact but the approach is general and can be easily extended to any prior setup. The proposed method is illustrated using simulation studies.