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ROC (Receiver Operating Characteristic) analyses are considered under a variety of assumptions concerning the distributions of a measurement <i>X</i> 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 <i>w</i> 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 <i>c</i> used for classification as well as the error characteristics used to assess the quality of the classification.