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

Area of Science:

• Statistics
• Computational Science

Background:

• Selecting relevant predictors is critical in nonparametric regression, especially with numerous variables.
• Existing methods face challenges in efficiently identifying optimal covariate subsets for accurate modeling.

Purpose of the Study:

• To propose a novel Bayesian nonparametric regression model for simultaneous curve-fitting and variable selection.
• To enhance the interpretability of regression functions using the smoothing spline ANOVA framework.
• To develop robust methods for hyperparameter selection that control false positive rates in variable selection.

Main Methods:

• Utilizing a Bayesian nonparametric approach combined with smoothing spline ANOVA.
• Implementing stochastic search variable selection through Markov Chain Monte Carlo (MCMC) sampling.
• Developing a technique for hyperparameter selection to manage the long-run false positive rate.

Main Results:

• The proposed model effectively performs curve-fitting and variable selection in nonparametric regression.
• The smoothing spline ANOVA framework facilitates interpretable decomposition of the regression function.
• The developed hyperparameter selection technique ensures reliable variable selection by controlling false positives.

Conclusions:

• The Bayesian nonparametric regression model offers a powerful tool for complex data analysis and model building.
• The method provides a principled approach to variable selection, improving model performance and interpretability.
• The application in emulating a two-phase fluid flow model demonstrates practical utility in scientific computing.