Universal Convergence of Kriging

• Activity Number: 213 - Lead with Statistics in Uncertainty Quantification
• Type: Invited
• Date/Time: Monday, July 30, 2018 : 2:00 PM to 3:50 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): C. F. Jeff Wu* and Rui Tuo and Wenjia Wang
• Companies: Georgia Institute of Technology and Chinese Academy of Sciences and Georgia Institute of Technology
• Keywords: Gaussian Process modeling; Uniform convergence; Space-filling designs; Radial basis functions

Abstract

Kriging based on Gaussian random fields is widely used in reconstructing unknown functions. The kriging method has pointwise predictive distributions which are computationally simple. However, in many applications one would like to predict for a range of untried points simultaneously. In this work we obtain some error bounds for the (simple) kriging predictor under the uniform metric. It works for a scattered set of input points in an arbitrary dimension, and also covers the case where the covariance function of the Gaussian process is misspecified. These results lead to a better understanding of the rate of convergence of kriging under the Gaussian or the Matérn correlation functions, the relationship between space-filling designs and kriging models, and the robustness of the Matérn correlation functions.