Fair Scores for Multivariate Gaussian Forecasts

probabilitystatistics theorydata analysis, statistics and probability

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Asymptotic Methods in Statistics

Series comments: Abstract: In ensemble-based probabilistic weather forecasting, it is often necessary to verify multidimensional predictions using verification scores. Such multidimensional quantities can be, for example, values of a weather variable taken at different locations, a set of several weather quantities, or simply the two-dimensional wind vector. Assuming multivariate normality of the forecasts, we determine the dependence of two different verification measures on the ensemble size and provide their sample size-adjusted fair versions. We demonstrate the usefulness of the application of fair scores using real weather forecasts and simulation studies, also examining their robustness with respect to deviations from normality.