  This paper considers the computer model calibration problem and provides a
general frequentist solution. Under the proposed framework, the data model is
semi-parametric with a nonparametric discrepancy function which accounts for
any discrepancy between the physical reality and the computer model. In an
attempt to solve a fundamentally important (but often ignored) identifiability
issue between the computer model parameters and the discrepancy function, this
paper proposes a new and identifiable parametrization of the calibration
problem. It also develops a two-step procedure for estimating all the relevant
quantities under the new parameterization. This estimation procedure is shown
to enjoy excellent rates of convergence and can be straightforwardly
implemented with existing software. For uncertainty quantification,
bootstrapping is adopted to construct confidence regions for the quantities of
interest. The practical performance of the proposed methodology is illustrated
through simulation examples and an application to a computational fluid
dynamics model.
