Doctor of Philosophy
E. O. George
William T. Smith
In this dissertation, we propose hybrid-testing procedures as a general class of methods that simultaneously addresses the problems of procedure selection and multiple testing. At each hierarchical level, the results from each testing are summarized as a set of p-values andempirical Bayesianprobabilities (EBPs) of the corresponding null hypotheses. Prior knowledge of the properties of the primary test statistics isused to construct an algorithm which uses the distributional assumption of the tests to determine weights for combining the EBPs. The combined EBPs can be used as a measure of statistical significance that adjusts formultiple-testing while accounting for the several assumptions used in thehierarchy of hypothesis-testing procedures. In the second part of this dissertation, we apply the development of the first part for constructing a hybrid testing procedure that incorporates assumptions and information about graphical network relations into the analysis of gene expression data based on the biological knowledge that neighboring genesshare biological functions. The degree of correlation between genes is taken into account via similar prior probabilities for neighboring genes. We show that combining these different elements not only improve statistical power, butalso provide a better framework through which gene expressioncan be properly analyzed. We use a series of simulations to compare our approach withother published methods and demonstrate that our method has more statisticalpower.
Dissertation or thesis originally submitted to the local University of Memphis Electronic Theses & dissertation (ETD) Repository.
Fofana, Demba, "On Some Bayesian and Empirical Bayes Procedures for Analyzing Gene Expression Data" (2016). Electronic Theses and Dissertations. 1387.