Extending $\mathrm{F}_1$ metric, probabilistic approach

This article explores the extension of well-known $\mathrm{F}_1$ score used for assessing the performance of binary classifiers. We propose the new metric using probabilistic interpretation of precision, recall, specificity, and negative predictive value. We describe its properties and compare it to common metrics. Then we demonstrate its behavior in edge cases of the confusion matrix. Finally, the properties of the metric are tested on binary classifier trained on the real dataset.