• Login
    View Item 
    •   Home
    • Office of Sponsored Research (OSR)
    • KAUST Funded Research
    • Publications Acknowledging KAUST Support
    • View Item
    •   Home
    • Office of Sponsored Research (OSR)
    • KAUST Funded Research
    • Publications Acknowledging KAUST Support
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Browse

    All of KAUSTCommunitiesIssue DateSubmit DateThis CollectionIssue DateSubmit Date

    My Account

    Login

    Quick Links

    Open Access PolicyORCID LibguideTheses and Dissertations LibguideSubmit an Item

    Statistics

    Display statistics

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

    • CSV
    • RefMan
    • EndNote
    • BibTex
    • RefWorks
    Type
    Article
    Authors
    Allmaras, Moritz
    Bangerth, Wolfgang
    Linhart, Jean Marie
    Polanco, Javier
    Wang, Fang
    Wang, Kainan
    Webster, Jennifer
    Zedler, Sarah
    KAUST Grant Number
    KUS-C1-016-04
    Date
    2013-02-11
    Online Publication Date
    2013-02-11
    Print Publication Date
    2013-01
    Permanent link to this record
    http://hdl.handle.net/10754/598234
    
    Metadata
    Show full item record
    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.
    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.
    Publisher
    Society for Industrial & Applied Mathematics (SIAM)
    Journal
    SIAM Review
    DOI
    10.1137/100788604
    ae974a485f413a2113503eed53cd6c53
    10.1137/100788604
    Scopus Count
    Collections
    Publications Acknowledging KAUST Support

    entitlement

     
    DSpace software copyright © 2002-2023  DuraSpace
    Quick Guide | Contact Us | KAUST University Library
    Open Repository is a service hosted by 
    Atmire NV
     

    Export search results

    The export option will allow you to export the current search results of the entered query to a file. Different formats are available for download. To export the items, click on the button corresponding with the preferred download format.

    By default, clicking on the export buttons will result in a download of the allowed maximum amount of items. For anonymous users the allowed maximum amount is 50 search results.

    To select a subset of the search results, click "Selective Export" button and make a selection of the items you want to export. The amount of items that can be exported at once is similarly restricted as the full export.

    After making a selection, click one of the export format buttons. The amount of items that will be exported is indicated in the bubble next to export format.