A Measure of Predictive Sharpness for Probabilistic Models

Abstract: This paper introduces a measure of predictive sharpness for probabilistic models, capturing the extent to which predictive mass departs from uniformity and concentrates over narrower subsets of the domain. For discrete settings, the measure is defined by cumulatively quantifying deviation from uniformity, taking into account both exclusion of outcomes and concentration of probability mass. For continuous settings, we develop an integral representation based on a monotone rearrangement of the predictive density. In supplementary material, we establish mathematical properties of the measure, derive formulas for forward and inverse domain transformations to support cross-domain comparisons, and provide an analysis of the relationship of the measure with entropy and variance.