A sequential approach for stochastic computer model calibration and prediction

Computer models are widely used to simulate complex and costly real processes and systems. When the computer model is used to assess and certify the real system for decision making, it is often important to calibrate the computer model so as to improve the model's predictive accuracy. A sequential approach is proposed in this paper for stochastic computer model calibration and prediction. More precisely, we propose a surrogate based Bayesian approach for stochastic computer model calibration which accounts for various uncertainties including the calibration parameter uncertainty in the follow up prediction and computer model analysis. We derive the posterior distribution of the calibration parameter and the predictive distributions for both the real process and the computer model which quantify the calibration and prediction uncertainty and provide the analytical calibration and prediction results. We also derive the predictive distribution of the discrepancy term between the real process and the computer model that can be used to validate the computer model. Furthermore, in order to efficiently use limited data resources to obtain a better calibration and prediction performance, we propose a two-stage sequential approach which can effectively allocate the limited resources. The accuracy and efficiency of the proposed approach are illustrated by the numerical examples.