Additive Gaussian Process for Computer Models With Qualitative and Quantitative Factors

ABSTRACT

Computer experiments with qualitative and quantitative factors occur frequently in various applications in science and engineering. Analysis of such experiments is not yet completely resolved. In this work, we propose an additive Gaussian process model for computer experiments with qualitative and quantitative factors. The proposed method considers an additive correlation structure for qualitative factors, and assumes that the correlation function for each qualitative factor and the correlation function of quantitative factors are multiplicative. It inherits the flexibility of unrestrictive correlation structure for qualitative factors by using the hypersphere decomposition, embracing more flexibility in modeling the complex systems of computer experiments. The merits of the proposed method are illustrated by several numerical examples and a real data application. Supplementary materials for this article are available online.

KEYWORDS:

• Additive model
• Computer experiment
• Fractional factorial design
• Hypersphere decomposition
• Kriging

Supplementary Materials

The supplementary material for this article contains the following: (1) proof of Theorem 1, (2) Matlab codes for implementation of the proposed method, and (3) data from the real application in Section 5.

Acknowledgments

The authors thank the editor, the associate editor, and two referees for their insightful comments. Lin is supported by the Natural Sciences and Engineering Research Council of Canada. Deng is supported by the National Science of Foundation of United States.