A Theoretical Framework for Calibration in Computer Models: Parametrization, Estimation and Convergence Properties

doi:10.1137/151005841

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	A Theoretical Framework for Calibration in Computer Models: Parametrization, Estimation and Convergence Properties
	Tuo, Rui1 ; Wu, C. F. Jeff 2
	2016
发表期刊	SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION
ISSN	2166-2525
卷号	4 期号:1 页码:767-795
摘要	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 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.
关键词	computer experiments uncertainty quantification Gaussian process reproducing kernel Hilbert space
DOI	10.1137/151005841
语种	英语
资助项目	Office 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研究方向	Mathematics ; Physics
WOS类目	Mathematics, Interdisciplinary Applications ; Physics, Mathematical
WOS记录号	WOS:000407996700030
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/26440
专题	系统科学研究所
通讯作者	Tuo, Rui
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Georgia Inst Technol, Sch Ind & Syst Engn, Atlanta, GA 30332 USA
推荐引用方式 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.