- Library Home /
- Search Collections /
- Open Collections /
- Browse Collections /
- UBC Theses and Dissertations /
- Geometric study on Bayesian statistics and random walks...
Open Collections
UBC Theses and Dissertations
UBC Theses and Dissertations
Geometric study on Bayesian statistics and random walks in the quarter plane Jiang, Ruichao
Abstract
In this dissertation, we apply geometric methods on probability theory and statistics. In the first half, using information geometry, we propose a new prior distribution in Bayesian statistics. We calculate the Weyl prior for the univariate Gaussian family and multivariate Gaussian family. The Weyl prior for the univariate Gaussian family turns out to be the uniform distribution, which is different from the Jeffreys prior. In the second half, we investigate the random walks in the quarter plane and we prove an upper bound 24 for the finite Galois groups associated with walks with ] rational coefficients. We also give explicit criteria on the finiteness of the Galois groups using division polynomial. These criteria are compactly expressed in terms of Eisenstein invariants and Frobenius invariants.
Item Metadata
| Title |
Geometric study on Bayesian statistics and random walks in the quarter plane
|
| Creator | |
| Supervisor | |
| Publisher |
University of British Columbia
|
| Date Issued |
2021
|
| Description |
In this dissertation, we apply geometric methods on probability theory and statistics. In the first half, using information geometry, we propose a new prior distribution in Bayesian statistics. We calculate the Weyl prior for the univariate Gaussian family and multivariate Gaussian family. The Weyl prior for the univariate Gaussian family turns out to be the uniform distribution, which is different from the Jeffreys prior. In the second half, we investigate the random walks in the quarter plane and we prove an upper bound 24 for the finite Galois groups associated with walks with ] rational coefficients. We also give explicit criteria on the finiteness of the Galois groups using division polynomial. These criteria are compactly expressed in terms of Eisenstein invariants and Frobenius invariants.
|
| Genre | |
| Type | |
| Language |
eng
|
| Date Available |
2021-08-30
|
| Provider |
Vancouver : University of British Columbia Library
|
| Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
|
| DOI |
10.14288/1.0401796
|
| URI | |
| Degree | |
| Program | |
| Affiliation | |
| Degree Grantor |
University of British Columbia
|
| Graduation Date |
2021-09
|
| Campus | |
| Scholarly Level |
Graduate
|
| Rights URI | |
| Aggregated Source Repository |
DSpace
|
Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International