Fast bayesian variable screening using correlation thresholds

We propose a fast Bayesian variable screening method for Normal regression models using thresholds on Pearson and partial correlation coefficients. Although the proposed method is based on the computation of correlation coefficients, it is derived using purely Bayesian arguments obtained from thresholds on Bayes factors and posterior model odds. The proposed method can be used to screen out the “non-important" covariates and reduce the size of the model space even in cases when the number of covariates is larger than the sample size. Then, on the reduced model space, obtained from the proposed approach, more accurate, traditional, computer-intensive, Bayesian variable selectionmethods can be implemented, if needed. We focus on the use of g-priors where Bayes factors can be obtained analytically and the corresponding correlation threshold computations are exact. Nevertheless, the approach is general and can be easily extended to any prior setup. The proposed method is illustrated using simulated examples.