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A Theoretical Framework for Calibration in Computer Models: Parametrization, Estimation and Convergence Properties
Tuo, Rui1; Wu, C. F. Jeff2
2016
Source PublicationSIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION
ISSN2166-2525
Volume4Issue:1Pages:767-795
AbstractCalibration 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 L-2-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 L-2-inconsistent calibration. This L-2-inconsistency can be remedied by modifying the original estimation procedure. A novel calibration method, called L-2 calibration, is proposed, proven to be L-2-consistent, and enjoys optimal convergence rate. A numerical example and some mathematical analysis are used to illustrate the source of the L-2-inconsistency problem.
Keywordcomputer experiments uncertainty quantification Gaussian process reproducing kernel Hilbert space
DOI10.1137/151005841
Language英语
Funding ProjectOffice of Advanced Scientific Computing Research ; U.S. Department of Energy[ERKJ259] ; UT-Battelle, LLC[De-AC05-00OR22725] ; National Center for Mathematics and Interdisciplinary Sciences, CAS ; NSFC[11271355] ; NSF[DMS-1308424] ; DOE[DE-SC0010548]
WOS Research AreaMathematics ; Physics
WOS SubjectMathematics, Interdisciplinary Applications ; Physics, Mathematical
WOS IDWOS:000407996700030
PublisherSIAM PUBLICATIONS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/26440
Collection系统科学研究所
Corresponding AuthorTuo, Rui
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
2.Georgia Inst Technol, Sch Ind & Syst Engn, Atlanta, GA 30332 USA
Recommended Citation
GB/T 7714
Tuo, Rui,Wu, C. F. Jeff. A Theoretical Framework for Calibration in Computer Models: Parametrization, Estimation and Convergence Properties[J]. SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION,2016,4(1):767-795.
APA Tuo, Rui,&Wu, C. F. Jeff.(2016).A Theoretical Framework for Calibration in Computer Models: Parametrization, Estimation and Convergence Properties.SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION,4(1),767-795.
MLA Tuo, Rui,et al."A Theoretical Framework for Calibration in Computer Models: Parametrization, Estimation and Convergence Properties".SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION 4.1(2016):767-795.
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