Conditional Probabilities, Relative Operating Characteristics, and Relative Operating Levels

Conditional Probabilities, Relative Operating Characteristics, and Relative Operating Levels

The relative operating characteristic (ROC) curve is a highly flexible method for representing the quality of dichotomous, categorical, continuous, and probabilistic forecasts. The method is based on ratios that measure the proportions of events and nonevents for which warnings were provided. These ratios provide estimates of the probabilities that an event will be forewarned and that an incorr...

Conditional and Relative Multifractal Spectra

In the study of the involved geometry of singular distributions the use of fractal and multifractal analysis has shown results of outstanding signi cance So far the investigation has focussed on structures produced by one single mechanism which were analyzed with respect to the ordinary metric or volume Most prominent examples include self similar measures and attractors of dynamical systems In...

RELATIVE INFORMATION FUNCTIONAL OF RELATIVE DYNAMICAL SYSTEMS

 In this paper by use of mathematical modeling of an observer [14,15] the notion of relative information functional for relative dynamical systemson compact metric spaces is presented. We extract the information function ofan ergodic dynamical system (X,T) from the relative information of T fromthe view point of observer χX, where X denotes the base space of the system.We also generalize the in...

Improvements in the use of the Relative Operating Characteristic (ROC) statistics

Smooth Receiver Operating Characteristics (smROC) Curves

Supervised learning algorithms perform common tasks including classification, ranking, scoring, and probability estimation. We investigate how scoring information, often produced by these models, is utilized by an evaluation measure. The ROC curve represents a visualization of the ranking performance of classifiers. However, they ignore the scores which can be quite informative. While this igno...