Publication Date
2021
Document Type
Dissertation/Thesis
First Advisor
González, Bárbara
Degree Name
Ph.D. (Doctor of Philosophy)
Legacy Department
Department of Mathematical Sciences
Abstract
Bayesian statistics is a prevalent and important field in statistics that assigns Bayesian probabilities, which represent a state of knowledge, to unknown quantities. We study Bayesian statistics with its applications through two projects in this report.
In the first project, we investigate the reasons that the Bayesian estimator of the tail probability is always higher than the frequentist estimator. Sufficient conditions for this phenomenon are established by looking at Taylor series approximations about the tail and by using Jensen's Inequality, both of which point to the convexity of the distribution function.
The second project is about redefining the Bayesian information criterion (BIC) in the model selection procedure using the effective sample size, which has a better theoretical foundation in the circumstance that mixed-effects models involve. Numerical experiment results are also given by comparing the performance of our new BIC with other widely used BICs.
Recommended Citation
Shen, Nan, "Bayesian Tail Probability Estimation and Model Selection" (2021). Graduate Research Theses & Dissertations. 7660.
https://huskiecommons.lib.niu.edu/allgraduate-thesesdissertations/7660
Extent
81 pages
Language
eng
Publisher
Northern Illinois University
Rights Statement
In Copyright
Rights Statement 2
NIU theses are protected by copyright. They may be viewed from Huskie Commons for any purpose, but reproduction or distribution in any format is prohibited without the written permission of the authors.
Media Type
Text
