Journal
ANNALS OF STATISTICS
Volume 43, Issue 6, Pages 2331-2352Publisher
INST MATHEMATICAL STATISTICS-IMS
DOI: 10.1214/15-AOS1314
Keywords
Computer experiments; uncertainty quantification; semiparametric efficiency; reproducing kernel Hilbert space
Categories
Funding
- Office of Advanced Scientific Computing Research
- U.S. Department of Energy [ERKJ259]
- National Center for Mathematics and Interdisciplinary Sciences, CAS
- NSF [DMS-13-08424]
- DOE [DE-SC0010548]
- UT-Battelle, LLC [De-AC05-00OR22725]
- NSFC [11271355]
- U.S. Department of Energy (DOE) [DE-SC0010548] Funding Source: U.S. Department of Energy (DOE)
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1308424] Funding Source: National Science Foundation
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Many computer models contain unknown parameters which need to be estimated using physical observations. Tuo and Wu (2014) show that the calibration method based on Gaussian process models proposed by Kennedy and O'Hagan [J. R. Stat. Soc. Ser. B. Stat. Methodol. 63 (2001) 425-464] may lead to an unreasonable estimate for imperfect computer models. In this work, we extend their study to calibration problems with stochastic physical data. We propose a novel method, called the L-2 calibration, and show its semiparametric efficiency. The conventional method of the ordinary least squares is also studied. Theoretical analysis shows that it is consistent but not efficient. Numerical examples show that the proposed method outperforms the existing ones.
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