Linear Parameter Uncertainty Quantification using Surrogate Gaussian Processes

We 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.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2020

Author dc:creator

• Macatula, Romcholo Yulo

Chair dc:contributor.committeechair

• Chung, Matthias

Committee members dc:contributor.committeemember

• Gramacy, Robert B.
• Bardsley, Johnathan M.
• Gugercin, Serkan

• uncertainty quantification
• surrogate models
• linear parameter estimation
• tomography
• bayesian
• gaussian process

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

vt_gsexam:26965

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/99411