ROC (Receiver Operating Characteristic) 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 (Area Under the Curve), the cutoff c used for classification as well as the error characteristics used to assess the quality of the classification.