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Revisiting Empirical Bayes Methods and Applications to Special Types of Data

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.

Identiferoai:union.ndltd.org:uottawa.ca/oai:ruor.uottawa.ca:10393/42340
Date29 June 2021
CreatorsDuan, Xiuwen
ContributorsAlvo, Mayer
PublisherUniversité d'Ottawa / University of Ottawa
Source SetsUniversité d’Ottawa
LanguageEnglish
Detected LanguageEnglish
TypeThesis
Formatapplication/pdf

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