A measure-theoretic approach to Bayesian hypothesis testing and inversion with geophysical data
Abstract/Contents
- Abstract
- Today, most geophysical hypothesis testing and inverse problems are formulated using conditional probability and Bayes' Theorem. In this dissertation, we argue that measure-theoretic principles provide a more natural alternative to hypothesis testing and inverse problems. First, we present the theory behind this measure-theoretic formulation of inverse problems. We also compare it to the conditional probability and conjunction of information inverse problem formulations. Then, we apply the hypothesis testing formulation to compare a numerical model of river delta sedimentation to laboratory experiments. This comparison quantitatively shows that the numerical delta model cannot capture the experimental channel dynamics. Finally, we apply the inversion formulation to determine the geological origins of a zone of fractured shale bedrock in the Rocky Mountains of Colorado. We invert electrical resistivity tomography data to estimate the dip angle of the fracture zone, which shows that two of the six proposed fracturing mechanisms are inconsistent with the data. Together, the theory and applications developed in this dissertation show that measure-theoretic formulations can help solve larger and more complicated Bayesian inference problems than existing methods.
Description
| Type of resource | text |
|---|---|
| Form | electronic resource; remote; computer; online resource |
| Extent | 1 online resource. |
| Place | California |
| Place | [Stanford, California] |
| Publisher | [Stanford University] |
| Copyright date | 2022; ©2022 |
| Publication date | 2022; 2022 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Miltenberger, Alex |
|---|---|
| Degree supervisor | Mukerji, Tapan, 1965- |
| Thesis advisor | Mukerji, Tapan, 1965- |
| Thesis advisor | Caers, Jef |
| Thesis advisor | Knight, Rosemary (Rosemary Jane), 1953- |
| Degree committee member | Caers, Jef |
| Degree committee member | Knight, Rosemary (Rosemary Jane), 1953- |
| Associated with | Stanford University, Department of Geophysics |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Alex M. Miltenberger. |
|---|---|
| Note | Submitted to the Department of Geophysics. |
| Thesis | Thesis Ph.D. Stanford University 2022. |
| Location | https://purl.stanford.edu/vs655kw5485 |
Access conditions
- Copyright
- © 2022 by Alex Miltenberger
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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