Ranking and estimation of exchangeable means in balanced and unbalanced models: A Bayesian approach
Abstract
In Berger and Deely (1986), a hierarchical Bayesian approach to Ranking and Selection was adopted to address problems in one-way classification models. This thesis is concerned with applying the hierarchical Bayesian methodology to higher way classification problems. First, we generalize the Bayesian ANOVA test in one-way models, which is concerned with equality of all means, to allow for simultaneous testing of many hypotheses involving equality of subsets of means. We also consider certain estimation problems such as the estimation of the largest mean and its variance, etc. Second, we make use of orthogonal properties of the design and the concept of posterior decomposition to extend the methodology to higher way classification problems. We discuss in detail some two-way models including the unbalanced additive case and the balanced model with interactions. Finally, we consider the special case of comparison of two treatments. Substantial simplifications are found which greatly reduce the complexity of the calculations, sometimes even leading to closed form solutions. Also efficient Monte Carlo methods for carrying out the necessary high dimensional integrations are developed, and illustrated on several examples.
Degree
Ph.D.
Advisors
Berger, Purdue University.
Subject Area
Statistics
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