Computer model calibration with confidence and consistency

Matthew Plumlee

doi:10.1111/rssb.12314

Computer model calibration with confidence and consistency

Matthew Plumlee^*

^*Corresponding author for this work

Industrial Engineering and Management Sciences

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

The paper proposes and examines a calibration method for inexact models. The method produces a confidence set on the parameters that includes the best parameter with a desired probability under any sample size. Additionally, this confidence set is shown to be consistent in that it excludes suboptimal parameters in large sample environments. The method works and the results hold with few assumptions; the ideas are maintained even with discrete input spaces or parameter spaces. Computation of the confidence sets and approximate confidence sets is discussed. The performance is illustrated in a simulation example as well as two real data examples.

Original language	English (US)
Pages (from-to)	519-545
Number of pages	27
Journal	Journal of the Royal Statistical Society. Series B: Statistical Methodology
Volume	81
Issue number	3
DOIs	https://doi.org/10.1111/rssb.12314
State	Published - Jul 2019

Keywords

Frequentist
Inverse problem
Model discrepancy
Model inadequacy
Model misspecification
Non-linear regression
Uncertainty quantification

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1111/rssb.12314

Cite this

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title = "Computer model calibration with confidence and consistency",

abstract = "The paper proposes and examines a calibration method for inexact models. The method produces a confidence set on the parameters that includes the best parameter with a desired probability under any sample size. Additionally, this confidence set is shown to be consistent in that it excludes suboptimal parameters in large sample environments. The method works and the results hold with few assumptions; the ideas are maintained even with discrete input spaces or parameter spaces. Computation of the confidence sets and approximate confidence sets is discussed. The performance is illustrated in a simulation example as well as two real data examples.",

keywords = "Frequentist, Inverse problem, Model discrepancy, Model inadequacy, Model misspecification, Non-linear regression, Uncertainty quantification",

author = "Matthew Plumlee",

note = "Funding Information: The author gratefully acknowledges National Science Foundation award 1833195 and the Issac Newton Institute for support during the production of this work. The author also thanks Dan Apley, Barry Nelson, Anthony O{\textquoteright}Hagan, J. P. Gosling, Judy Jin, Wenbo Sun, two reviewers, the Associate Editor and the Joint Editor for their helpful comments and ideas towards this research. Publisher Copyright: {\textcopyright} 2019 Royal Statistical Society",

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N2 - The paper proposes and examines a calibration method for inexact models. The method produces a confidence set on the parameters that includes the best parameter with a desired probability under any sample size. Additionally, this confidence set is shown to be consistent in that it excludes suboptimal parameters in large sample environments. The method works and the results hold with few assumptions; the ideas are maintained even with discrete input spaces or parameter spaces. Computation of the confidence sets and approximate confidence sets is discussed. The performance is illustrated in a simulation example as well as two real data examples.

AB - The paper proposes and examines a calibration method for inexact models. The method produces a confidence set on the parameters that includes the best parameter with a desired probability under any sample size. Additionally, this confidence set is shown to be consistent in that it excludes suboptimal parameters in large sample environments. The method works and the results hold with few assumptions; the ideas are maintained even with discrete input spaces or parameter spaces. Computation of the confidence sets and approximate confidence sets is discussed. The performance is illustrated in a simulation example as well as two real data examples.

KW - Frequentist

KW - Inverse problem

KW - Model discrepancy

KW - Model inadequacy

KW - Model misspecification

KW - Non-linear regression

KW - Uncertainty quantification

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JF - Journal of the Royal Statistical Society. Series B: Statistical Methodology

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Computer model calibration with confidence and consistency

Abstract

Keywords

ASJC Scopus subject areas

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