Empirical Bayesian Analysis for Computer Experiments Involving Finite-Difference Codes

Computer experiments are increasingly used in scientific investigations as substitutes for physical experiments in cases where the latter are difficult or impossible to perform. A computer experiment consists of several runs of a computer model or “code” for the purpose of better understanding the input → output relationship. One practical difficulty in the use of these models is that a single run may require a prohibitive amount of computational resources in some situations. A recent approach uses statistical approximations as less expensive surrogates for such computer codes; these provide both point predictors and uncertainty characterization of the outputs. A widely used class of computer codes is the finite-difference solvers of differential equations, which produce multivariate output (e.g., time series). The finitedifference relationship underpins the statistical model proposed here, and we show that this strategy has clear computational and accuracy advantages over a direct multivariate extension of the popular scalar modeling methodology.