A Theoretical Framework for Calibration in Computer Models: Parametrization, Estimation and Convergence Properties
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© 2016 Sharif Rahman. Calibration parameters in deterministic computer experiments are those attributes that cannot be measured or are not available in physical experiments. Kennedy and O'Hagan [M.C. Kennedy and A. O'Hagan, J. R. Stat. Soc. Ser. B Stat. Methodol., 63 (2001), pp. 425-464] suggested an approach to estimating 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 Kennedy-O'Hagan (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 L2 calibration, is proposed, 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.
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