A Framework for Controlling Sources of Inaccuracy in Gaussian Process Emulation of Deterministic Computer Experiments

Computer experiments have become ubiquitous in science and engineering. Commonly, runs of these simulations demand considerable time and computing, making experimental design extremely important in gaining high quality information with limited time and resources. Broad principles of experimental design are proposed and justified which ensure high nominal, numeric, and parameter estimation accuracy for Gaussian process emulation of deterministic simulations. The space-filling properties "small fill distance" and "large separation distance" are only weakly conflicting and ensure well-controlled nominal, numeric, and parameter estimation errors. Nonstationarity indicates a greater density of experimental inputs in regions of the input space with more quickly decaying correlation, while nonconstant regression functions indicate a balancing of traditional design features with space-fillingness. This work provides robust, rigorously justified, and practically useful overarching qualitative principles for scientists and engineers selecting combinations of simulation inputs with high information content.