A theoretical framework for calibration in computer models: parametrization, estimation and convergence properties

Calibration parameters in deterministic computer experiments are those attributes that cannot be measured or available in physical experiments. Kennedy and O'Hagan citekennedy2001bayesian suggested an approach to estimate them by using data from physical experiments and computer simulations. A theoretical framework is given which allows us to study the issues of parameter identifiability and estimation. We define the L2-consistency for calibration as a justification for calibration methods. It is shown that a simplified version of the original KO method leads to asymptotically L2-inconsistent calibration. This L2-inconsistency can be remedied by modifying the original estimation procedure. A novel calibration method, called the L2 calibration, is proposed and proven to be L2-consistent and enjoys optimal convergence rate. A numerical example and some mathematical analysis are used to illustrate the source of the L2-inconsistency problem.