Optimal neyman-pearson classification under Bayesian uncertainty models

A Bayesian modeling framework over an uncertainty class of underlying distributions has been used to derive an optimal MMSE error estimator for arbitrary classifiers and an optimal Bayesian classification rule that minimizes expected error, both relative to the overall misclassification rate. In this work, we use the same Bayesian framework to formulate a Neyman-Pearson based approach that optimizes relative to true and false positive rates. True and false positive rates are often of more practical use than the misclassification rate in medical applications, meanwhile the Neyman-Pearson theory does not require modeling or knowledge of the prior class probabilities.