Double-robust Bayesian variable selection and model prediction with spherically symmetric error

Response surface methodology has been known as an effective tool for improving an overall manufacturing process where quality requirements are fulfilled. This work proposes a double-robust Bayesian modeling method that can simultaneously cope with variable selection, model form uncertainty, and non-normality for quality prediction. Double robustness is achieved by specifying the class of spherically symmetric distributions for the errors and accounting for model form uncertainty through Bayesian model averaging. Furthermore, with a special choice in the sub-harmonic priors for the regression coefficients, a closed-form expression of the marginal posterior distribution of each candidate model is obtained, which is not only free of the error distributions (other than spherical symmetry) but also can be easily computed using standard software. To provide a better interpretation of the model, a special prior is specified for the model space to maintain and reflect the hierarchical or structural relationships among input variables. The proposed Bayesian method has the properties of variable selection consistency and prediction consistency under Bayesian model averaging. Through numerical experiments and a case study, the proposed double-robust Bayesian modeling method is shown to achieve results superior to those of the existing established methods in prediction and variable selection in linear models under different types of error distributions.