Scoring Rules for Forecast Verification

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Discrimination ability of the Energy score (2013, background): “For the case of predictive densities, both univariate and multivariate, a number of scores have been proposed and discussed, see for instance [9] and [12].”
Kullback–Leibler Divergence as a Forecast Skill Score with Classic Reliability–Resolution–Uncertainty Decomposition (2010, background): “Note that this is the original definition by Brier (1950). Nowadays, the Brier score is almost always defined as half the value of (2) (Ahrens and Walser 2008).”
Generalization of the Ignorance Score: Continuous Ranked Version and Its Decomposition (2012, background): “Roulston and Smith (2002) introduced the ignorance score (IGN) as the fundamental information-based measure, whose importance was confirmed by Benedetti (2010). Recently, Weijs et al. (2010a) showed that the IGN can be decomposed into easily interpretable reliability, resolution, and uncertainty com”
Empirical Evaluation of Hierarchical Ground‐Motion Models: Score Uncertainty and Model Weighting (2017, background): “The local score is arguably the only score that strictly complies with the scientific method: it assesses a model with only the observed and not the unobserved (Benedetti, 2010, section 2).”