Date of Award
Doctor of Philosophy
Ebenezer O. George
This dissertation addresses two types of problems in Applied Statistics. The first deals with the development of a procedure for estimating the correlation structure of RNA-Seq. data and the second type involves introducing a model that can be used to estimate significance of Genesets based on count data such as RNA-Seq. The approach we adopt is to model the RNA-Seq. data by exchangeable negative multinomial distribution. In the first Chapter, we give an overview of the structure of the dissertation, introduce some definition and also introduce the Exchangeable NegativeMultinomial Distribution resulting from relaxing the independence of the Multinomial distribution to exchangeability. It is demonstrated that the proposed model can be characterized by infinitely many parameters that form a completely monotone sequence. In Chapter 3, A weighted least squares algorithm is derived for a special case of the distribution for estimating the parameters for a finite sample. A likelihood ratio test is developed to show the dierence between treatments that follow this distribution. Chapter 4 is dedicated to a simulation study conducted to illustrate the distribution, showing the mean and variance for some select values of p1, p2, p3, and which are parameters of the model. A full likelihood procedure is described which can be used to investigate correlated and overdispersed count data common in bio-medical sciences. In the end, the introduced distribution is applied to analyze a Geneset containing 10 genes and 24 samples for lung cancer patients.
dissertation or thesis originally submitted to the local University of Memphis Electronic Theses & dissertation (ETD) Repository.
Kusi-Appiah, Akwasi Opoku, "On the Exhangeable Negative Multinomial Distribution and Applications to Analysis of RNA-Seq. Data" (2016). Electronic Theses and Dissertations. 1485.