Parametric modeling of receiver operating characteristics curves

Receiver operating characteristics (ROC) curves play a pivotal role in the analyses of data collected in applications involving machine vision, machine learning and clinical diagnostics. The importance of ROC curves lies in the fact that all decision-making strategies rely on the interpretations of the curves and features extracted from them. Such analyses become simple and straightforward if it is possible to have a statistical fit for the empirical ROC curve. A methodology is developed and demonstrated to obtain a parametric fit for the ROC curves using multiple tools in statistics such as chi square testing, bootstrapping (parametric and non-parametric) and t-testing. Relying on three data sets and an ensemble of density functions used in modeling sensor and econometric data, statistical modeling of the ROC curves (best fit) is accomplished. While the reported research relied on simulated data sets, the approaches implemented and demonstrated in this work can easily be adapted to data collected in clinical as well as non-clinical settings.