  Many computer models contain unknown parameters which need to be estimated
using physical observations. Kennedy and O'Hagan (2001) shows that the
calibration method based on Gaussian process models proposed by Kennedy and
O'Hagan (2001) may lead to unreasonable estimate for imperfect computer models.
In this work, we extend their study to calibration problems with stochastic
physical data. We propose a novel method, called the $L_2$ calibration, and
show its semiparametric efficiency. The conventional method of the ordinary
least squares is also studied. Theoretical analysis shows that it is consistent
but not efficient. Numerical examples show that the proposed method outperforms
the existing ones.
