  Computer models are commonly used to represent a wide range of real systems,
but they often involve some unknown parameters. Estimating the parameters by
collecting physical data becomes essential in many scientific fields, ranging
from engineering to biology. However, most of the existing methods are
developed under the assumption that the physical data contains homoscedastic
measurement errors. Motivated by an experiment of plant relative growth rates
where replicates are available, we propose a new calibration method for inexact
computer models with heteroscedastic measurement errors. Asymptotic properties
of the parameter estimators are derived, and a goodness-of-fit test is
developed to detect the presence of heteroscedasticity. Numerical examples and
empirical studies demonstrate that the proposed method not only yields accurate
parameter estimation, but it also provides accurate predictions for physical
data in the presence of both heteroscedasticity and model misspecification.
