File:Scoring functions.gif

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English: The dashed black line represents the forecaster's true belief, the x-axis is their actual prediction, and the y-axis the expected score given their true belief.

Note also: • The red line is the linear scoring rule, which just gives you the probability you assigned to the right outcome as score.

We see that it is not "proper" -- that is, the highest value is usually given by predicting close to 0 or 1, as opposed to your true belief.

For the other three functions, note that they all have their maxima at the true belief -- your best strategy is to be truthful. They are: • Orange line: spherical scoring rule • Purple line: Brier score • Green line: log score (you may recognize the shape of this curve. Because the expected log score is in fact the Shannon entropy of the underlying variable)

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Date
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Author Jacoblagerros

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27 August 2019

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current10:00, 27 August 2019Thumbnail for version as of 10:00, 27 August 2019300 × 300 (846 KB)JacoblagerrosCross-wiki upload from en.wikipedia.org

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