Bayesian calibration of stochastic computer models

Computer models are widely used to simulate real processes. Within the computer model, there always exist some parameters which are unobservable in the real process but need to be specified in the computer model. The procedure to adjust these unknown parameters in order to fit the model to observed data and improve its predictive capability is known as calibration. In traditional calibration, once the optimal calibration parameter set is obtained, it is treated as known for future prediction. Calibration parameter uncertainty introduced from estimation is not accounted for. We will present a Bayesian calibration approach for stochastic computer models. We account for these additional uncertainties and derive the predictive distribution for the real process. Two numerical examples are used to illustrate the accuracy of the proposed method.