ROC Analyses Based on Measuring Evidence

ROC analyses are considered under a variety of assumptions concerning the distributions of a measurement $X$ in two populations. These include the binormal model as well as nonparametric models where little is assumed about the form of distributions. The methodology is based on a characterization of statistical evidence which is dependent on the specification of prior distributions for the unknown population distributions as well as for the relevant prevalence $w$ of the disease in a given population. In all cases, elicitation algorithms are provided to guide the selection of the priors. Inferences are derived for the AUC as well as the cutoff $c$ used for classification and the associated error characteristics.