Linear Parameter Uncertainty Quantification using Surrogate Gaussian Processes

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dc.contributor.authorMacatula, Romcholo Yuloen
dc.contributor.committeechairChung, Matthiasen
dc.contributor.committeememberGramacy, Robert B.en
dc.contributor.committeememberBardsley, Johnathan M.en
dc.contributor.committeememberGugercin, Serkanen
dc.contributor.departmentMathematicsen
dc.date.accessioned2020-07-24T11:50:15Zen
dc.date.available2020-07-24T11:50:15Zen
dc.date.issued2020-07-21en
dc.description.abstractWe consider uncertainty quantification using surrogate Gaussian processes. We take a previous sampling algorithm and provide a closed form expression of the resulting posterior distribution. We extend the method to weighted least squares and a Bayesian approach both with closed form expressions of the resulting posterior distributions. We test methods on 1D deconvolution and 2D tomography. Our new methods improve on the previous algorithm, however fall short in some aspects to a typical Bayesian inference method.en
dc.description.abstractgeneralParameter uncertainty quantification seeks to determine both estimates and uncertainty regarding estimates of model parameters. Example of model parameters can include physical properties such as density, growth rates, or even deblurred images. Previous work has shown that replacing data with a surrogate model can provide promising estimates with low uncertainty. We extend the previous methods in the specific field of linear models. Theoretical results are tested on simulated computed tomography problems.en
dc.description.degreeMaster of Scienceen
dc.format.mediumETDen
dc.identifier.othervt_gsexam:26965en
dc.identifier.urihttp://hdl.handle.net/10919/99411en
dc.publisherVirginia Techen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectuncertainty quantificationen
dc.subjectsurrogate modelsen
dc.subjectlinear parameter estimationen
dc.subjecttomographyen
dc.subjectbayesianen
dc.subjectgaussian processen
dc.titleLinear Parameter Uncertainty Quantification using Surrogate Gaussian Processesen
dc.typeThesisen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.levelmastersen
thesis.degree.nameMaster of Scienceen

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