Minimally Corrective, Approximately Recovering Priors to Correct Expert Judgement in Bayesian Parameter Estimation

Bayesian 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.

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

2015

Author dc:creator

• May, Thomas Joseph

Chair dc:contributor.committeechair

• Zietsman, Lizette

Committee members dc:contributor.committeemember

• Borggaard, Jeffrey T.
• Rossi, John F.

• Bayesian Parameter Estimation
• Minimally Corrective Priors
• Distributed Parameters
• Elliptic Equation
• Karhunen-Loeve Theorem.

Statement dc:rights

• In Copyright

Licence dc:rights.uri

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

Dc Identifier Other

vt_gsexam:5180

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/54593