Empirical Bayes methods have been around for a long time and have a wide range of
applications. These methods provide a way in which historical data can be aggregated
to provide estimates of the posterior mean. This thesis revisits some of the empirical
Bayesian methods and develops new applications. We first look at a linear empirical Bayes estimator and apply it on ranking and symbolic data. Next, we consider
Tweedie’s formula and show how it can be applied to analyze a microarray dataset.
The application of the formula is simplified with the Pearson system of distributions.
Saddlepoint approximations enable us to generalize several results in this direction.
The results show that the proposed methods perform well in applications to real data
sets.
| Identifer | oai:union.ndltd.org:uottawa.ca/oai:ruor.uottawa.ca:10393/42340 |
| Date | 29 June 2021 |
| Creators | Duan, Xiuwen |
| Contributors | Alvo, Mayer |
| Publisher | Université d'Ottawa / University of Ottawa |
| Source Sets | Université d’Ottawa |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
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