Two Bayesian variable screening procedures

In this paper, two Bayesian variable screening procedures (FBRPN and BRPN) are proposed to obtain meaningful protective and risk factors in fast and sequential ways in models with a linear component such as the GLMs to avoid multicollinearity. The two final fitted models from the procedures are compared to find the most efficient model and relatively uncorrelated representative variables of the original predictors. The Bayesian procedures are illustrated in two examples, with comparisons to the stepwise and best subsets regression methods. Simulation studies with no true models are carried out to show how different correlation structures and sample sizes can affect the final fitted models from different procedures, and the Bayesian procedures produce relatively unrelated representative variables, which fit the connotation of “independent variables”‘. Cross-validation comparisons with stepwise, LASSO, LAR, random forest and NNET methods are made based on the generated Efron diabetes data, which contains 64 dummy variables and provides a fair base for comparisons of different methods. The theory and practical issues are discussed, and applications of the procedures in big data analysis are envisioned.