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 finite-difference 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.