UBC Theses and Dissertations
Geometric study on Bayesian statistics and random walks in the quarter plane Jiang, Ruichao
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.
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Attribution-NonCommercial-NoDerivatives 4.0 International