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Computational measure theoretic approach to inverse sensitivity analysis: methods and analysis

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dc.contributor.authorButler, Troy Daniel, author
dc.contributor.authorEstep, Donald, advisor
dc.date.accessioned2024-03-13T18:50:55Z
dc.date.available2024-03-13T18:50:55Z
dc.date.issued2009
dc.description.abstractWe consider the inverse problem of quantifying the uncertainty of inputs to a finite dimensional map, e.g. determined implicitly by solution of a nonlinear system, given specified uncertainty in a linear functional of the output of the map. The uncertainty in the output functional might be suggested by experimental error or imposed as part of a sensitivity analysis. We describe this problem probabilistically, so that the uncertainty in the quantity of interest is represented by a random variable with a known distribution, and we assume that the map from the input space to the quantity of interest is smooth. We derive an efficient method for determining the unique solution to the problem of inverting through a many-to-one map by computing set-valued inverses of the input space which combines a forward sensitivity analysis with the Implicit Function Theorem. We then derive an efficient computational measure theoretic approach to further invert into the entire input space resulting in an approximate probability measure on the input space.
dc.description.abstractWe provide detailed error analysis for inverse problems involving nonlinear ordinary differential equations and semilinear elliptic partial differential equations.
dc.format.mediumborn digital
dc.format.mediumdoctoral dissertations
dc.identifierETDF_Butler_2009_3385166.pdf
dc.identifier.urihttps://hdl.handle.net/10217/237617
dc.languageEnglish
dc.language.isoeng
dc.publisherColorado State University. Libraries
dc.relation.ispartof2000-2019
dc.rightsCopyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.
dc.rights.licensePer the terms of a contractual agreement, all use of this item is limited to the non-commercial use of Colorado State University and its authorized users.
dc.subjectBayesian inference
dc.subjectImplicit Function Theorem
dc.subjectinverse sensitivity
dc.subjectposteriori analysis
dc.subjectsemilinear elliptic
dc.subjectmechanics
dc.subjectmathematics
dc.subjectstatistics
dc.titleComputational measure theoretic approach to inverse sensitivity analysis: methods and analysis
dc.typeText
dcterms.rights.dplaThis Item is protected by copyright and/or related rights (https://rightsstatements.org/vocab/InC/1.0/). You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
thesis.degree.disciplineMathematics
thesis.degree.grantorColorado State University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy (Ph.D.)

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