Estimating Parameters in Physical Models through Bayesian Inversion: A Complete Example

Handle URI:
http://hdl.handle.net/10754/598234
Title:
Estimating Parameters in Physical Models through Bayesian Inversion: A Complete Example
Authors:
Allmaras, Moritz; Bangerth, Wolfgang; Linhart, Jean Marie; Polanco, Javier; Wang, Fang; Wang, Kainan; Webster, Jennifer; Zedler, Sarah
Abstract:
All mathematical models of real-world phenomena contain parameters that need to be estimated from measurements, either for realistic predictions or simply to understand the characteristics of the model. Bayesian statistics provides a framework for parameter estimation in which uncertainties about models and measurements are translated into uncertainties in estimates of parameters. This paper provides a simple, step-by-step example-starting from a physical experiment and going through all of the mathematics-to explain the use of Bayesian techniques for estimating the coefficients of gravity and air friction in the equations describing a falling body. In the experiment we dropped an object from a known height and recorded the free fall using a video camera. The video recording was analyzed frame by frame to obtain the distance the body had fallen as a function of time, including measures of uncertainty in our data that we describe as probability densities. We explain the decisions behind the various choices of probability distributions and relate them to observed phenomena. Our measured data are then combined with a mathematical model of a falling body to obtain probability densities on the space of parameters we seek to estimate. We interpret these results and discuss sources of errors in our estimation procedure. © 2013 Society for Industrial and Applied Mathematics.
Citation:
Allmaras M, Bangerth W, Linhart JM, Polanco J, Wang F, et al. (2013) Estimating Parameters in Physical Models through Bayesian Inversion: A Complete Example. SIAM Review 55: 149–167. Available: http://dx.doi.org/10.1137/100788604.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Review
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
7-Feb-2013
DOI:
10.1137/100788604
Type:
Article
ISSN:
0036-1445; 1095-7200
Sponsors:
The work of the first, third, fifth, and eighth authors was supported by award KUS-C1-016-04 from the KingAbdullah University of Science and Technology. The work of the seventh author was supported byU.S. Department of Homeland Security grant 2008-DN-077-ARI001-02.The work of this author was supported by NSF award DMS-0604778, U.S. Department of Energy grant DE-FG07-07ID14767, U.S. Department of HomelandSecurity grant 2008-DN-077-ARI001-02, award KUS-C1-016-04 from the King Abdullah Universityof Science and Technology, and an Alfred P. Sloan Research Fellowship.
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Full metadata record

DC FieldValue Language
dc.contributor.authorAllmaras, Moritzen
dc.contributor.authorBangerth, Wolfgangen
dc.contributor.authorLinhart, Jean Marieen
dc.contributor.authorPolanco, Javieren
dc.contributor.authorWang, Fangen
dc.contributor.authorWang, Kainanen
dc.contributor.authorWebster, Jenniferen
dc.contributor.authorZedler, Sarahen
dc.date.accessioned2016-02-25T13:17:06Zen
dc.date.available2016-02-25T13:17:06Zen
dc.date.issued2013-02-07en
dc.identifier.citationAllmaras M, Bangerth W, Linhart JM, Polanco J, Wang F, et al. (2013) Estimating Parameters in Physical Models through Bayesian Inversion: A Complete Example. SIAM Review 55: 149–167. Available: http://dx.doi.org/10.1137/100788604.en
dc.identifier.issn0036-1445en
dc.identifier.issn1095-7200en
dc.identifier.doi10.1137/100788604en
dc.identifier.urihttp://hdl.handle.net/10754/598234en
dc.description.abstractAll mathematical models of real-world phenomena contain parameters that need to be estimated from measurements, either for realistic predictions or simply to understand the characteristics of the model. Bayesian statistics provides a framework for parameter estimation in which uncertainties about models and measurements are translated into uncertainties in estimates of parameters. This paper provides a simple, step-by-step example-starting from a physical experiment and going through all of the mathematics-to explain the use of Bayesian techniques for estimating the coefficients of gravity and air friction in the equations describing a falling body. In the experiment we dropped an object from a known height and recorded the free fall using a video camera. The video recording was analyzed frame by frame to obtain the distance the body had fallen as a function of time, including measures of uncertainty in our data that we describe as probability densities. We explain the decisions behind the various choices of probability distributions and relate them to observed phenomena. Our measured data are then combined with a mathematical model of a falling body to obtain probability densities on the space of parameters we seek to estimate. We interpret these results and discuss sources of errors in our estimation procedure. © 2013 Society for Industrial and Applied Mathematics.en
dc.description.sponsorshipThe work of the first, third, fifth, and eighth authors was supported by award KUS-C1-016-04 from the KingAbdullah University of Science and Technology. The work of the seventh author was supported byU.S. Department of Homeland Security grant 2008-DN-077-ARI001-02.The work of this author was supported by NSF award DMS-0604778, U.S. Department of Energy grant DE-FG07-07ID14767, U.S. Department of HomelandSecurity grant 2008-DN-077-ARI001-02, award KUS-C1-016-04 from the King Abdullah Universityof Science and Technology, and an Alfred P. Sloan Research Fellowship.en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.subjectBayesian estimation techniquesen
dc.subjectParameter estimationen
dc.subjectPosterior probability distributionen
dc.subjectPriorsen
dc.titleEstimating Parameters in Physical Models through Bayesian Inversion: A Complete Exampleen
dc.typeArticleen
dc.identifier.journalSIAM Reviewen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
kaust.grant.numberKUS-C1-016-04en
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