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dc.contributor.authorAguilar, Oscar
dc.contributor.authorAllmaras, Moritz
dc.contributor.authorBangerth, Wolfgang
dc.contributor.authorTenorio, Luis
dc.date.accessioned2016-02-28T06:08:32Z
dc.date.available2016-02-28T06:08:32Z
dc.date.issued2015-01
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.
dc.identifier.issn0036-1445
dc.identifier.issn1095-7200
dc.identifier.doi10.1137/130929230
dc.identifier.urihttp://hdl.handle.net/10754/599732
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.
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.
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)
dc.subjectBayesian inference
dc.subjectData analysis
dc.subjectFrequentist inference
dc.subjectMaximum likelihood
dc.subjectModel validation
dc.subjectNonlinear regression
dc.subjectParameter estimation
dc.subjectResidual analysis
dc.subjectSurrogate models
dc.titleStatistics of Parameter Estimates: A Concrete Example
dc.typeArticle
dc.identifier.journalSIAM Review
dc.contributor.institutionIowa State University, Ames, United States
dc.contributor.institutionSiemens AG, Munich, Germany
dc.contributor.institutionTexas A and M University, College Station, United States
dc.contributor.institutionColorado School of Mines, Golden, United States
kaust.grant.numberKUS-C1-016-04


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