Convex Combination of Gaussian Processes for Bayesian Analysis of Deterministic Computer Experiments

Abstract

The use of Gaussian processes is a popular approach to analyzing data from computer experiments. Combining more than one Gaussian process in a surrogate model for computer simulation could prove useful when there is uncertainty regarding the family of correlation functions, or when one wishes to characterize both global trends and finer details, all in the same model. We suggest a fully Bayesian treatment of the problem, taking advantage of MCMC sampling methods and providing point estimates and Bayesian credible intervals with a high degree of success, according to simulation results. We then provide guidelines for choosing a suitable batch sequential maximum entropy design for these models. Supplementary materials for this article are available online.

KEY WORDS:

• Kriging
• Maximum entropy
• MCMC

ACKNOWLEDGMENT

This research was sponsored by the U.S.–Israel Binational Science Foundation under Grant No. 2008218.