Multivariate binormal mixtures for semi-parametric inference on ROC curves

Abstract

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. (C) 2011 The Korean Statistical Society. Published by Elsevier B.V. All rights reserved.