Calibration parameters in deterministic computer experiments are those attributes that cannot be measured or available in physical experiments or observations. Kennedy-O’Hagan (2001) suggested an approach to estimate them by using data from physical experiments and computer simulations. A new theoretical framework is given which allows us to study the issues of parameter identifiability and estimation. It is shown that a simplified version of the original KO method leads to asymptotically inconsistent calibration. A novel calibration method, called the L2 calibration, is proposed and proven to be consistent and enjoys optimal convergence rate. The asymptotic results of L2 calibration for stochastic physical systems are also studied. It is proved that the L2 calibration estimator is asymptotically normal and semi-parametric efficient. This work also investigates the asymptotic properties of the ordinary least squares method.
(joint work with C. F. Jeff Wu, Georgia Institute of Technology)