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Entropy 2015, 17(8), 5450-5471; doi:10.3390/e17085450

Probabilistic Forecasts: Scoring Rules and Their Decomposition and Diagrammatic Representation via Bregman Divergences

Crop and Soil Systems, SRUC, West Mains Road, Edinburgh, EH9-3JG, UK
These authors contributed equally to this work.
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Author to whom correspondence should be addressed.
Academic Editor: Benjamin L. Ruddell
Received: 18 May 2015 / Revised: 27 July 2015 / Accepted: 28 July 2015 / Published: 31 July 2015
(This article belongs to the Special Issue Applications of Information Theory in the Geosciences)
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Abstract

A scoring rule is a device for evaluation of forecasts that are given in terms of the probability of an event. In this article we will restrict our attention to binary forecasts. We may think of a scoring rule as a penalty attached to a forecast after the event has been observed. Thus a relatively small penalty will accrue if a high probability forecast that an event will occur is followed by occurrence of the event. On the other hand, a relatively large penalty will accrue if this forecast is followed by non-occurrence of the event. Meteorologists have been foremost in developing scoring rules for the evaluation of probabilistic forecasts. Here we use a published meteorological data set to illustrate diagrammatically the Brier score and the divergence score, and their statistical decompositions, as examples of Bregman divergences. In writing this article, we have in mind environmental scientists and modellers for whom meteorological factors are important drivers of biological, physical and chemical processes of interest. In this context, we briefly draw attention to the potential for probabilistic forecasting of the within-season component of nitrous oxide emissions from agricultural soils. View Full-Text
Keywords: scoring rule; binary forecast; Brier score; divergence score; Bregman divergence; N2O emissions models scoring rule; binary forecast; Brier score; divergence score; Bregman divergence; N2O emissions models
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Hughes, G.; Topp, C.F. Probabilistic Forecasts: Scoring Rules and Their Decomposition and Diagrammatic Representation via Bregman Divergences. Entropy 2015, 17, 5450-5471.

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