A better Beta for the H measure of classification performance

The area under the ROC curve is widely used as a measure of performance of classification rules. However, it has recently been shown that the measure is fundamentally incoherent, in the sense that it treats the relative severities of misclassifications differently when different classifiers are used. To overcome this, Hand (2009) proposed the $H$ measure, which allows a given researcher to fix the distribution of relative severities to a classifier-independent setting on a given problem. This note extends the discussion, and proposes a modified standard distribution for the $H$ measure, which better matches the requirements of researchers, in particular those faced with heavily unbalanced datasets, the $Beta(\pi_1+1,\pi_0+1)$ distribution. [Preprint submitted at Pattern Recognition Letters]