Analysis Methods for Computer Experiments: How to Assess and What Counts?

Abstract

Statistical methods based on a regression model plus a zero-mean Gaussian process (GP) have been widely used for predicting the output of a deterministic computer code. There are many suggestions in the literature for how to choose the regression component and how to model the correlation structure of the GP. This article argues that comprehensive, evidence-based assessment strategies are needed when comparing such modeling options. Otherwise, one is easily misled. Applying the strategies to several computer codes shows that a regression model more complex than a constant mean either has little impact on prediction accuracy or is an impediment. The choice of correlation function has modest effect, but there is little to separate two common choices, the power exponential and the Matérn, if the latter is optimized with respect to its smoothness. The applications presented here also provide no evidence that a composite of GPs provides practical improvement in prediction accuracy. A limited comparison of Bayesian and empirical Bayes methods is similarly inconclusive. In contrast, we find that the effect of experimental design is surprisingly large, even for designs of the same type with the same theoretical properties.