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Parameter Estimation via Bayesian Inversion: Theory, Methods, and Applications

Soncini, Ryan (2014) Parameter Estimation via Bayesian Inversion: Theory, Methods, and Applications. Master's Thesis, University of Pittsburgh. (Unpublished)

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Uncertainty quantification is becoming an increasingly important area of investigation in the field of computational simulations. An understanding in the confidence of a simulation result requires information concerning the uncertainties associated with individual sub-models. The development of mathematical models for physical systems resides in the interpretation of experimental results. Inherent to physically interesting mathematical models is the occurrence of unobservable model parameters. The resolution of information concerning model parameters is typically performed through the use of least-squares regression analysis; however, least-squares analysis does not provide adequate information concerning the confidence which may be placed in the parameter estimates. Bayesian inversion provides quantifiable information concerning the confidence which may be placed in the parameter estimates allowing for overall simulation uncertainty quantification. Here, the application of Bayesian statistics to the general discrete inverse problem is presented. Following the presentation of the Bayesian formulation of the general discrete inverse problem, the procedure is applied to two scientifically interesting inverse problems: the reversible-reaction diffusion inverse problem and the Arrhenius inverse problem. The Arrhenius inverse problem is solved using a novel approach developed here. The novel approach is compared to other probabilistic and deterministic approaches to assess the validity of the method.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Soncini, Ryan rms78@pitt.eduRMS78
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee MemberRobertson, Annerbertson@pitt.eduRBERTSON
Committee MemberGaldi, Giovannigaldi@pitt.eduGALDI
Thesis AdvisorZunino, Paolopaz13@pitt.eduPAZ13
Date: 29 January 2014
Date Type: Publication
Defense Date: 21 November 2013
Approval Date: 29 January 2014
Submission Date: 26 November 2013
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Number of Pages: 95
Institution: University of Pittsburgh
Schools and Programs: Swanson School of Engineering > Mechanical Engineering
Degree: MS - Master of Science
Thesis Type: Master's Thesis
Refereed: Yes
Uncontrolled Keywords: Bayesian Inversion, Parameter Estimation
Date Deposited: 29 Jan 2014 16:19
Last Modified: 15 Nov 2016 14:16


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