Statistical Tests for Cross-Validation of Kriging Models

Abstract

We derive new statistical tests for leave-one-out cross-validation of Kriging models. Graphically, we present these tests as scatterplots augmented with confidence intervals. We may wish to avoid extrapolation, which we define as prediction of the output for a point that is a vertex of the convex hull of the given input combinations. Moreover, we may use bootstrapping to estimate the true variance of the Kriging predictor. The resulting tests (with or without extrapolation or bootstrapping) have type-I and type-II error probabilities, which we estimate through Monte Carlo experiments. To illustrate the application of our tests, we use an example with two inputs and the popular borehole example with eight inputs.

Keywords: validation, cross-validation, Kriging, Gaussian process, extrapolation, convex hull, Monte Carlo

JEL Classification: C0, C1, C9, C15, C44