Optimal Calibration for Computer Model Prediction with Finite Samples
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This paper considers the computer model prediction in a non-asymptotic frequentist framework. Two main issues arise for the prediction: (1) many computer models are inadequate for physical systems and (2) only finite samples of physical observations are available for estimating model discrepancy and calibrating unknown parameters in computer models. In this work, we propose the optimal calibration and give exact statistical guarantees in the sense that the predictive mean squared error is minimized with the optimal calibration for any finite samples. We give an equivalent formulation of the 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 [J. R. Stat. Soc. Ser. B. Stat. Methodol. 63 (2001) 425-464]. Numerical simulations and a real data example show that the proposed calibration outperforms the existing ones in terms of the prediction.
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