Handle URI:
http://hdl.handle.net/10754/599732
Title:
Statistics of Parameter Estimates: A Concrete Example
Authors:
Aguilar, Oscar; Allmaras, Moritz; Bangerth, Wolfgang; Tenorio, Luis
Abstract:
© 2015 Society for Industrial and Applied Mathematics. Most mathematical models include parameters that need to be determined from measurements. The estimated values of these parameters and their uncertainties depend on assumptions made about noise levels, models, or prior knowledge. But what can we say about the validity of such estimates, and the influence of these assumptions? This paper is concerned with methods to address these questions, and for didactic purposes it is written in the context of a concrete nonlinear parameter estimation problem. We will use the results of a physical experiment conducted by Allmaras et al. at Texas A&M University [M. Allmaras et al., SIAM Rev., 55 (2013), pp. 149-167] to illustrate the importance of validation procedures for statistical parameter estimation. We describe statistical methods and data analysis tools to check the choices of likelihood and prior distributions, and provide examples of how to compare Bayesian results with those obtained by non-Bayesian methods based on different types of assumptions. We explain how different statistical methods can be used in complementary ways to improve the understanding of parameter estimates and their uncertainties.
Citation:
Aguilar O, Allmaras M, Bangerth W, Tenorio L (2015) Statistics of Parameter Estimates: A Concrete Example. SIAM Review 57: 131–149. Available: http://dx.doi.org/10.1137/130929230.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Review
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
Jan-2015
DOI:
10.1137/130929230
Type:
Article
ISSN:
0036-1445; 1095-7200
Sponsors:
The work of this author was partially supported by award KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).The work of this author was partially supported by NSF grant DMS-0914987.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorAguilar, Oscaren
dc.contributor.authorAllmaras, Moritzen
dc.contributor.authorBangerth, Wolfgangen
dc.contributor.authorTenorio, Luisen
dc.date.accessioned2016-02-28T06:08:32Zen
dc.date.available2016-02-28T06:08:32Zen
dc.date.issued2015-01en
dc.identifier.citationAguilar O, Allmaras M, Bangerth W, Tenorio L (2015) Statistics of Parameter Estimates: A Concrete Example. SIAM Review 57: 131–149. Available: http://dx.doi.org/10.1137/130929230.en
dc.identifier.issn0036-1445en
dc.identifier.issn1095-7200en
dc.identifier.doi10.1137/130929230en
dc.identifier.urihttp://hdl.handle.net/10754/599732en
dc.description.abstract© 2015 Society for Industrial and Applied Mathematics. Most mathematical models include parameters that need to be determined from measurements. The estimated values of these parameters and their uncertainties depend on assumptions made about noise levels, models, or prior knowledge. But what can we say about the validity of such estimates, and the influence of these assumptions? This paper is concerned with methods to address these questions, and for didactic purposes it is written in the context of a concrete nonlinear parameter estimation problem. We will use the results of a physical experiment conducted by Allmaras et al. at Texas A&M University [M. Allmaras et al., SIAM Rev., 55 (2013), pp. 149-167] to illustrate the importance of validation procedures for statistical parameter estimation. We describe statistical methods and data analysis tools to check the choices of likelihood and prior distributions, and provide examples of how to compare Bayesian results with those obtained by non-Bayesian methods based on different types of assumptions. We explain how different statistical methods can be used in complementary ways to improve the understanding of parameter estimates and their uncertainties.en
dc.description.sponsorshipThe work of this author was partially supported by award KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).The work of this author was partially supported by NSF grant DMS-0914987.en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.subjectBayesian inferenceen
dc.subjectData analysisen
dc.subjectFrequentist inferenceen
dc.subjectMaximum likelihooden
dc.subjectModel validationen
dc.subjectNonlinear regressionen
dc.subjectParameter estimationen
dc.subjectResidual analysisen
dc.subjectSurrogate modelsen
dc.titleStatistics of Parameter Estimates: A Concrete Exampleen
dc.typeArticleen
dc.identifier.journalSIAM Reviewen
dc.contributor.institutionIowa State University, Ames, United Statesen
dc.contributor.institutionSiemens AG, Munich, Germanyen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
dc.contributor.institutionColorado School of Mines, Golden, United Statesen
kaust.grant.numberKUS-C1-016-04en
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