Optimal Calibration for Computer Model Prediction with Finite Samples
We consider a non-asymptotic frequentist framework for computer model prediction. This framework concerns two main issues: (1) many computer models are inadequate for physical systems and (2) only nite samples of physical observations are available for estimating model discrepancy and calibrating multivariate unknown parameters in computer models. We propose a method to achieve the optimal calibration and provide exact statistical guarantees in the sense that the predictive mean squared error is minimized with optimal calibration for any nite samples. We derive an equivalent formulation of optimal calibration which leads naturally to an iterative algorithm. The connection is built between the optimal calibration and the Bayesian calibration in Kennedy and O’Hagan. Numerical simulations and a real data example show that the proposed calibration outperforms the existing ones in terms of the prediction.