Contributions to the Analysis of Experiments Using Empirical Bayes Techniques

Abstract

Specifying a prior distribution for the large number of parameters in the linear statistical model is a difficult step in the Bayesian approach to the design and analysis of experiments. Here we address this difficulty by proposing the use of functional priors and then by working out important details for three and higher level experiments. One of the challenges presented by higher level experiments is that a factor can be either qualitative or quantitative. We propose appropriate correlation functions and coding schemes so that the prior distribution is simple and the results easily interpretable. The prior incorporates well known experimental design principles such as effect hierarchy and effect heredity, which helps to automatically resolve the aliasing problems experienced in fractional designs.

The second part of the thesis focuses on the analysis of optimization experiments. Not uncommon are designed experiments with their primary purpose being to determine optimal settings for all of the factors in some predetermined set. Here we distinguish between the two concepts of statistical significance and practical significance. We perform estimation via an empirical Bayes data analysis methodology that has been detailed in the recent literature. But then propose an alternative to the usual next step in determining optimal factor level settings. Instead of implementing variable or model selection techniques, we propose an objective function that assists in our goal of finding the ideal settings for all factors over which we experimented. The usefulness of the new approach is illustrated through the analysis of some real experiments as well as simulation.