Author ORCID Identifier

Year of Publication


Degree Name

Doctor of Philosophy (PhD)

Document Type

Doctoral Dissertation


Arts and Sciences



First Advisor

Dr. Richard Charnigo


This dissertation research is concentrated on the Contaminated Beta(CB) model and its application in micro-array data analysis. Modified Likelihood Ratio Test (MLRT) introduced by [Chen et al., 2001] is used for testing the omnibus null hypothesis of no contamination of Beta(1,1)([Dai and Charnigo, 2008]). We design constraints for two-component CB model, which put the mode toward the left end of the distribution to reflect the abundance of small p-values of micro-array data, to increase the test power. A three-component CB model might be useful when distinguishing high differentially expressed genes and moderate differentially expressed genes. If the null hypothesis above is rejected, we considered developing a method of testing the hypothesis of two-component vs three-component CB model. We first study CB model with one-parameter kernel distribution by fixing the other shape parameter across all the components. Using MLRT introduced by [Chen et al., 2004], we find the feasibility of this model after investigation. Then we consider a three-component CB model and designed constraints to guarantee the identifiability. We also study model selection and use sBIC introduced by [Drton and Plummer, 2017] to determine the number of components. We applied our tests and model to a toddler Down Syndrome data sets.

Digital Object Identifier (DOI)