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dc.contributor.authorMay, Thomas Josephen_US
dc.date.accessioned2015-07-24T08:00:23Z
dc.date.available2015-07-24T08:00:23Z
dc.date.issued2015-07-23en_US
dc.identifier.othervt_gsexam:5180en_US
dc.identifier.urihttp://hdl.handle.net/10919/54593
dc.description.abstractBayesian parameter estimation is a popular method to address inverse problems. However, since prior distributions are chosen based on expert judgement, the method can inherently introduce bias into the understanding of the parameters. This can be especially relevant in the case of distributed parameters where it is difficult to check for error. To minimize this bias, we develop the idea of a minimally corrective, approximately recovering prior (MCAR prior) that generates a guide for the prior and corrects the expert supplied prior according to that guide. We demonstrate this approach for the 1D elliptic equation or the elliptic partial differential equation and observe how this method works in cases with significant and without any expert bias. In the case of significant expert bias, the method substantially reduces the bias and, in the case with no expert bias, the method only introduces minor errors. The cost of introducing these small errors for good judgement is worth the benefit of correcting major errors in bad judgement. This is particularly true when the prior is only determined using a heuristic or an assumed distribution.en_US
dc.format.mediumETDen_US
dc.publisherVirginia Techen_US
dc.rightsThis Item is protected by copyright and/or related rights. Some uses of this Item may be deemed fair and permitted by law even without permission from the rights holder(s), or the rights holder(s) may have licensed the work for use under certain conditions. For other uses you need to obtain permission from the rights holder(s).en_US
dc.subjectBayesian Parameter Estimationen_US
dc.subjectMinimally Corrective Priorsen_US
dc.subjectDistributed Parametersen_US
dc.subjectElliptic Equationen_US
dc.subjectKarhunen-Loeve Theorem.en_US
dc.titleMinimally Corrective, Approximately Recovering Priors to Correct Expert Judgement in Bayesian Parameter Estimationen_US
dc.typeThesisen_US
dc.contributor.departmentMathematicsen_US
dc.description.degreeMSen_US
thesis.degree.nameMSen_US
thesis.degree.levelmastersen_US
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen_US
thesis.degree.disciplineMathematicsen_US
dc.contributor.committeechairZietsman, Lizetteen_US
dc.contributor.committeememberBorggaard, Jeffrey Ten_US
dc.contributor.committeememberRossi, John Fen_US


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