Mathematical Sciences: Bayesian Analysis of Two- and Higher-Way Models

The statistical problems of ranking and selection, hypothesis testing, estimation and prediction in two-way and higher-way layout experiments will be investigated from a Bayesian perspective. Hierarchical Bayesian procedures may be implemented for everyday use through the realization that only low-dimensional numerical integration is needed for many commonly used models and that the efficient computational methods to evaluate these integrals are available. The goals of this research are to characterize the multi-way classification problems, to provide hierarchical Bayesian solution for the models identified in the characterization, and to develop efficient algorithms to compute the required integrals needed to implement the Bayesian methodology.