An improved approach to Bayesian computer model calibration and prediction

We consider the problem of calibrating inexact computer models using experimental data. To compensate for the misspecification of the computer model, a discrepancy function is usually included and modeled via a Gaussian stochastic process (GaSP), leading to better results of prediction. The calibration parameters in the computer model, however, sometimes become unidentifiable in the GaSP model, and the calibrated computer model fits the experimental data poorly as a consequence. In this work, we propose the scaled Gaussian stochastic process (S-GaSP), a novel stochastic process for calibration and prediction. This new approach bridges the gap between two predominant methods, namely the $L_2$ calibration and GaSP calibration. A computationally feasible approach is introduced for this new model under the Bayesian paradigm. The S-GaSP model not only provides a general framework for calibration, but also enables the computer model to predict well regardless of the discrepancy function. Numerical examples are also provided to illustrate the connections and differences between this new model and other previous approaches.