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Equation 1 · Part 8 · Attribution: Tying One Event to a Changing Climate

Denominator: PR

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}}.
PR\mathrm{PR}

What this part means

The complete quantity below the fraction bar; it must be nonzero for this division.

Its job in the formula

PR occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

The passage around this formula

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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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

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Sources cited in the surrounding passage

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