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 parame...

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Main Author: May, Thomas Joseph
Other Authors: Mathematics
Format: Others
Published: Virginia Tech 2015
Subjects:
Online Access:http://hdl.handle.net/10919/54593
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spelling ndltd-VTETD-oai-vtechworks.lib.vt.edu-10919-545932020-09-29T05:44:25Z Minimally Corrective, Approximately Recovering Priors to Correct Expert Judgement in Bayesian Parameter Estimation May, Thomas Joseph Mathematics Zietsman, Lizette Borggaard, Jeffrey T. Rossi, John F. Bayesian Parameter Estimation Minimally Corrective Priors Distributed Parameters Elliptic Equation Karhunen-Loeve Theorem. 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. Master of Science 2015-07-24T08:00:23Z 2015-07-24T08:00:23Z 2015-07-23 Thesis vt_gsexam:5180 http://hdl.handle.net/10919/54593 In Copyright http://rightsstatements.org/vocab/InC/1.0/ ETD application/pdf Virginia Tech
collection NDLTD
format Others
sources NDLTD
topic Bayesian Parameter Estimation
Minimally Corrective Priors
Distributed Parameters
Elliptic Equation
Karhunen-Loeve Theorem.
spellingShingle Bayesian Parameter Estimation
Minimally Corrective Priors
Distributed Parameters
Elliptic Equation
Karhunen-Loeve Theorem.
May, Thomas Joseph
Minimally Corrective, Approximately Recovering Priors to Correct Expert Judgement in Bayesian Parameter Estimation
description 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. === Master of Science
author2 Mathematics
author_facet Mathematics
May, Thomas Joseph
author May, Thomas Joseph
author_sort May, Thomas Joseph
title Minimally Corrective, Approximately Recovering Priors to Correct Expert Judgement in Bayesian Parameter Estimation
title_short Minimally Corrective, Approximately Recovering Priors to Correct Expert Judgement in Bayesian Parameter Estimation
title_full Minimally Corrective, Approximately Recovering Priors to Correct Expert Judgement in Bayesian Parameter Estimation
title_fullStr Minimally Corrective, Approximately Recovering Priors to Correct Expert Judgement in Bayesian Parameter Estimation
title_full_unstemmed Minimally Corrective, Approximately Recovering Priors to Correct Expert Judgement in Bayesian Parameter Estimation
title_sort minimally corrective, approximately recovering priors to correct expert judgement in bayesian parameter estimation
publisher Virginia Tech
publishDate 2015
url http://hdl.handle.net/10919/54593
work_keys_str_mv AT maythomasjoseph minimallycorrectiveapproximatelyrecoveringpriorstocorrectexpertjudgementinbayesianparameterestimation
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