Probabilistic forecasts: scoring rules and their decomposition and diagrammatic representation via Bregman divergences

G Hughes, CFE Topp

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)5450 - 5471
Number of pages22
JournalEntropy
Volume17
Issue number8
DOIs
Publication statusFirst published - 2015

Fingerprint

divergence
decomposition
nitrous oxide
chemical process
agricultural soil
biological processes
forecast
penalty
evaluation

Bibliographical note

1023324

Keywords

  • Binary forecast
  • Bregman divergence score
  • Brier score
  • N2O emissions models
  • Scoring rule

Cite this

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Probabilistic forecasts: scoring rules and their decomposition and diagrammatic representation via Bregman divergences. / Hughes, G; Topp, CFE.

In: Entropy, Vol. 17, No. 8, 2015, p. 5450 - 5471.

Research output: Contribution to journalArticleResearchpeer-review

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AU - Hughes, G

AU - Topp, CFE

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AB - 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.

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