Some approaches to Bayesian design of experiments and microarray data analysis
Doctor of Philosophy
This thesis consists of three projects. The first project introduces methodology to design drug development studies in an optimal fashion. Optimality is defined in a decision-theoretic framework where the goal is expected utility maximization. We show how our approach outperforms some other conventional designs. The second project generalizes the hierarchical Gamma/Gamma model for microarray data analysis. We illustrate how our generalization improves the fit without increasing the model complexity, and how one can use it to find differentially expressed genes and to build a classifier. When the sample size is small our method finds more genes and classifies samples better than several standard methods. Only as the number of microarrays grows large competing methods detect more genes. The last project explores the use of L 2E partial density estimation as an exploratory technique in the context of microarray data analysis. We propose a heuristic that combines frequentist and Bayesian ideas. Our approach outperforms other competing methods when its assumptions hold, but it presents increased false positive rates when the assumptions do not hold.