Designing combined physical and computer experiments to maximize prediction accuracy

Combined designs for experiments involving a physical system and a simulator of the physical system are evaluated in terms of their accuracy of predicting the mean of the physical system. Comparisons are made among designs that are (1) locally optimal under the minimum integrated mean squared prediction error criterion for the combined physical system and simulator experiments, (2) locally optimal for the physical or simulator experiments, with a fixed design for the component not being optimized, (3) maximin augmented nested Latin hypercube, and (4) I-optimal for the physical system experiment and maximin Latin hypercube for the simulator experiment. Computational methods are proposed for constructing the designs of interest. For a large test bed of examples, the empirical mean squared prediction errors are compared at a grid of inputs for each test surface using a statistically calibrated Bayesian predictor based on the data from each design. The prediction errors are also studied for a test bed that varies only the calibration parameter of the test surface. Design recommendations are given.