  We consider the problem of calibrating an imperfect computer model using
experimental data. To compensate the misspecification of the computer model and
make more accurate predictions, a discrepancy function is often included and
modeled via a Gaussian stochastic process (GaSP). The calibrated computer model
alone, however, sometimes fits the experimental data poorly, as the calibration
parameters become unidentifiable. In this work, we propose the scaled Gaussian
stochastic process (S-GaSP), a novel stochastic process that bridges the gap
between two predominant methods, namely the $L_2$ calibration and the GaSP
calibration. It is shown that our approach performs well in both calibration
and prediction. A computationally feasible approach is introduced for this new
model under the Bayesian paradigm. Compared with the GaSP calibration, the
S-GaSP calibration enables the calibrated computer model itself to predict the
reality well, based on the posterior distribution of the calibration
parameters. Numerical comparisons of the simulated and real data are provided
to illustrate the connections and differences between the proposed S-GaSP and
other alternative approaches.

Methodology