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Published equation contexts

PR=p1p0,FAR=1−p0p1=1−1PR\mathrm{PR} = \frac{p_1}{p_0}, \qquad \mathrm{FAR} = 1 - \frac{p_0}{p_1} = 1 - \frac{1}{\mathrm{PR}}

Why this formula appears here

The standard output is a probability ratio, also called a risk ratio, comparing the annual probability of the event in the factual climate with its probability in the counterfactual one [ 3 ] . Writing those probabilities as the factual and counterfactual annual exceedance probabilities, PR=p1p0,FAR=1−p0p1=1−1PR\mathrm{PR} = \frac{p_1}{p_0}, \qquad \mathrm{FAR} = 1 - \frac{p_0}{p_1} = 1 - \frac{1}{\mathrm{PR}}. The fraction of attributable risk is a monotone transform of the ratio and contains no additional information. Its name invites a misreading that the field has warned about for two decades: it is not the probability that this event was caused by forcing, and it does not license the statement that a given fraction of the damage was anthropogenic in any individual case. It is a…

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With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.

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Published contexts (1)

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PR=p1p0,FAR=1−p0p1=1−1PR.\mathrm{PR} = \frac{p_1}{p_0}, \qquad \mathrm{FAR} = 1 - \frac{p_0}{p_1} = 1 - \frac{1}{\mathrm{PR}}.

Equation 1 · Earth & Climate

Attribution: Tying One Event to a Changing Climate

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

The standard output is a probability ratio, also called a risk ratio, comparing the annual probability of the event in the factual climate with its probability in the counterfactual one [ 3 ] . Writing those probabilities as the factual and counterfactual annual exceedance probabilities, PR=p1p0,FAR=1−p0p1=1−1PR\mathrm{PR} = \frac{p_1}{p_0}, \qquad \mathrm{FAR} = 1 - \frac{p_0}{p_1} = 1 - \frac{1}{\mathrm{PR}}. The fraction of attributable risk is a monotone transform of the ratio and contains no additional information. Its name invites a misreading that the field has warned about for two decades: it is not the probability that this event was caused by forcing, and it does not license the statement that a given fraction of the damage was anthropogenic in any individual case. It is a…

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