Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Department of Mathematics and Statistics

First Advisor

Christine M. Schubert Kabban, PhD.


In decision making, an optimal point represents the settings for which a classification system should be operated to achieve maximum performance. Clearly, these optimal points are of great importance in classification theory. Not only is the selection of the optimal point of interest, but quantifying the uncertainty in the optimal point and its performance is also important. The Youden index is a metric currently employed for selection and performance quantification of optimal points for classification system families. The Youden index quantifies the correct classification rates of a classification system, and its confidence interval quantifies the uncertainty in this measurement. This metric currently focuses on two or three classes, and only allows for the utility of correct classifications and the cost of total misclassifications to be considered. An alternative to this metric for three or more classes is a cost function which considers the sum of incorrect classification rates. This new metric is preferable as it can include class prevalences and costs associated with every classification. In multi-class settings this informs better decisions and inferences on optimal points. The work in this dissertation develops theory and methods for confidence intervals on a metric based on misclassfication rates, Bayes Cost, and where possible, the thresholds found for an optimal point using Bayes Cost. Hypothesis tests for Bayes Cost are also developed to test a classification systems performance or compare systems with an emphasis on classification systems involving three or more classes. Performance of the newly proposed methods is demonstrated with simulation.

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