Multivariate binormal mixtures for semi-parametric inference on ROC curves

A Receiver Operating Characteristic (ROC) curve reflects the performance of a system which decides between two competing actions in a test of statistical hypotheses. This paper addresses the inference on ROC curves for the following problem: How can one statistically validate the performance of a system with a claimed ROC curve, ROC0 say? Our proposed solution consists of two main components: first, a flexible family of distributions, namely the multivariate binormal mixtures, is proposed to account for intra-sample correlation and non-Gaussianity of the marginal distributions under both the null and alternative hypotheses. Second, a semi-parametric inferential framework is developed for estimating all unknown parameters based on a rank likelihood. Actual inference is carried out by running a Gibbs sampler until convergence, and subsequently, constructing a highest posterior density (HPD) set for the true but unknown ROC curve based on the Gibbs output. The proposed methodology is illustrated on several simulation studies and real data.