Contributions To Ancestral Inference For Supercritical Branching Processes And High-Dimensional Data Analysis

Abstract

This thesis is concerned with statistical methods that are relevant in the scientific study of gene expression data. It is customary in these areas to use microarray technology as a first step in identifying the genes that are differentially expressed followed by using quantitative polymerase chain reaction (qPCR) as a confirmatory tool. The first part of thesis addresses statistical analysis for qPCR data, while the second part of the thesis addresses the so-called large p, small n problem, using microarray gene expression data as the motivating example. Description of the gene expression profiles from PCR can be cast within the more general framework of ancestral inference for branching processes. Accordingly, part one of the thesis is devoted to the study of branching processes initiated by a random number of ancestors. We address issues concerning modeling, inference, and asymptotic justification of the proposed methodologies. The second part of the thesis focuses on microarray data, specifically developing multivariate techniques for identifying differentially expressed genes. The results can be viewed in the more general context of multiple hypothesis testing or the multivariate testing problem.