Online learning with the Continuous Ranked Probability Score for ensemble forecasting

International audienceEnsemble forecasting resorts to multiple individual forecasts to produce a discrete probability distribution which accurately represents the uncertainties. Before every forecast, a weighted empirical distribution function is derived from the ensemble, so as to minimize the Continuous Ranked Probability Score (CRPS). We apply online learning techniques, which have previously been used for deterministic forecasting, and we adapt them for the minimization of the CRPS. The proposed method theoretically guarantees that the aggregated forecast competes, in terms of CRPS, against the best weighted empirical distribution function with weights constant in time. This is illustrated on synthetic data. Besides, our study improves the knowledge of the CRPS expectation for model mixtures. We generalize results on the bias of the CRPS computed with ensemble forecasts, and propose a new scheme to achieve fair CRPS minimization , without any assumption on the distributions