Variable selection in Bayesian smoothing spline ANOVA models: Application to deterministic computer codes

With many predictors, choosing an appropriate subset of the covariates is a crucial-and difficult-step in nonparametric regression. We propose a Bayesian nonparametric regression model for curve fitting and variable selection. We use the smoothing splines ANOVA framework to decompose the regression function into interpretable main effect and interaction functions, and use stochastic search variable selection through Markov chain Monte Carlo sampling to search for models that fit the data well. We also show that variable selection is highly sensitive to hyperparameter choice, and develop a technique for selecting hyperparameters that control the long-run false-positive rate. We use our method to build an emulator for a complex computer model for two-phase fluid flow.