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. Here, 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 L _{2}consistency for calibration as a justification for calibration methods. It is shown that a simplified version of the original KO method leads to asymptotically L _{2}inconsistent calibration. This L _{2}inconsistency can be remedied by modifying the original estimation procedure. A novel calibration method, called the L _{2} calibration, is proposed and proven to be L _{2}consistent and enjoys optimal convergence rate. Furthermore a numerical example and some mathematical analysis are used to illustrate the source of the L _{2}inconsistency problem.
 Authors:

^{[1]};
^{[2]}
 Chinese Academy of Sciences (CAS), Beijing (China)
 Georgia Inst. of Technology, Atlanta, GA (United States)
 Publication Date:
 Report Number(s):
 DOEGT00105482
Journal ID: ISSN 21662525; FG0213ER26159
 Grant/Contract Number:
 SC0010548
 Type:
 Accepted Manuscript
 Journal Name:
 SIAM/ASA Journal on Uncertainty Quantification
 Additional Journal Information:
 Journal Volume: 4; Journal Issue: 1; Journal ID: ISSN 21662525
 Publisher:
 SIAM
 Research Org:
 Georgia Tech Research Corp., Atlanta, GA (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC21)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; computer experiments; uncertainty quantification; Gaussian process; reproducing kernel Hilbert space
 OSTI Identifier:
 1405142
Tuo, Rui, and Jeff Wu, C. F.. A Theoretical Framework for Calibration in Computer Models: Parametrization, Estimation and Convergence Properties. United States: N. p.,
Web. doi:10.1137/151005841.
Tuo, Rui, & Jeff Wu, C. F.. A Theoretical Framework for Calibration in Computer Models: Parametrization, Estimation and Convergence Properties. United States. doi:10.1137/151005841.
Tuo, Rui, and Jeff Wu, C. F.. 2016.
"A Theoretical Framework for Calibration in Computer Models: Parametrization, Estimation and Convergence Properties". United States.
doi:10.1137/151005841. https://www.osti.gov/servlets/purl/1405142.
@article{osti_1405142,
title = {A Theoretical Framework for Calibration in Computer Models: Parametrization, Estimation and Convergence Properties},
author = {Tuo, Rui and Jeff Wu, C. F.},
abstractNote = {Calibration parameters in deterministic computer experiments are those attributes that cannot be measured or available in physical experiments. Here, 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 L2consistency for calibration as a justification for calibration methods. It is shown that a simplified version of the original KO method leads to asymptotically L2inconsistent calibration. This L2inconsistency can be remedied by modifying the original estimation procedure. A novel calibration method, called the L2 calibration, is proposed and proven to be L2consistent and enjoys optimal convergence rate. Furthermore a numerical example and some mathematical analysis are used to illustrate the source of the L2inconsistency problem.},
doi = {10.1137/151005841},
journal = {SIAM/ASA Journal on Uncertainty Quantification},
number = 1,
volume = 4,
place = {United States},
year = {2016},
month = {7}
}