The Annals of Statistics

Efficient calibration for imperfect computer models

Rui Tuo and C. F. Jeff Wu

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist., Volume 43, Number 6 (2015), 2331-2352.

Dates
Received: April 2014
Revised: January 2015
First available in Project Euclid: 7 October 2015

Permanent link to this document
https://projecteuclid.org/euclid.aos/1444222077

Digital Object Identifier
doi:10.1214/15-AOS1314

Mathematical Reviews number (MathSciNet)
MR3405596

Zentralblatt MATH identifier
1326.62228

Subjects
Primary: 62P30: Applications in engineering and industry 62A01: Foundations and philosophical topics
Secondary: 62F12: Asymptotic properties of estimators

Keywords
Computer experiments uncertainty quantification semiparametric efficiency reproducing kernel Hilbert space

Citation

Tuo, Rui; Wu, C. F. Jeff. Efficient calibration for imperfect computer models. Ann. Statist. 43 (2015), no. 6, 2331--2352. doi:10.1214/15-AOS1314. https://projecteuclid.org/euclid.aos/1444222077


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