Hui Tao

Date of Award

2005

Level of Access Assigned by Author

Campus-Only Thesis

Degree Name

Master of Arts (MA)

Department

Mathematics

Advisor

Ramesh Gupta

Second Committee Member

Pushpa Gupta

Third Committee Member

Henrik Bresinsky

Abstract

A typical microarray experiment often involves comparisons of hundreds or thousands of genes. Since a large number of genes are compared, simple use of a significance test without adjustment for multiple comparison artifacts could lead to a large chance of false positive findings. In this thesis, we will study various methods that allow us to measure the overall error rate when testing multiple hypotheses. More specifically, we will examine the two models presented by Tsai et al. (2003). Both these models involve the distribution of the sum of identical Bernoulli random variables. Model I is derived under the assumption of independence of Bernoulli trials and Model II assumes non-independent Bernoulli trials. Because of the over-dispersion problem, this model is derived using a beta-binomial structure. Instead of using a beta-binomial model, we shall derive the exact distribution of the sum of non-independent and non-identically distributed Bernoulli random variables. This distribution will be used to compare the exact results with those obtained in Table-3 of Tsai et al. (2003).

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