ROC-анализ и калибровка скоринговых моделей на основе метрик точности второго порядка
The paper presents new metrics for the accuracy of second-order scoring models, which show the target scoring preference - better to diagnose " good" objects or better to identify "bad" ones, with the same predictive power determined by the generally accepted first-order metric - the Gini index. There are two metrics, they have both an integral representation and a numerical one. Using the proposed metrics, a method for triangulating the ROC curve is developed, which composes its properties into tree economically obvious parameters. A two-parameter universal hyperbolic family of model ROC curves is developed, which is isometrically homeomorphic to all possible practical ROC curves defined by first-and second-order metrics. This allowed us to offer universal calibration formulas for calculating the probability of default for scoring models, taking into account the target preferences of the models, left, right or neutral. We present finite explicit parametric formulas for the calibration problem, which is a key issue of the Internal Ratings Based Approach.