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Equation 1 · Part 10 · One Tree: The Statistics of Common Descent

Denominator: P(D mid M_IO)

K=P(D∣MUCA)P(D∣MIO)K = \frac{P(D \mid M_{\text{UCA}})}{P(D \mid M_{\text{IO}})}
P(D∣MIO)P(D \mid M_{\text{IO}})

What this part means

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

Its job in the formula

P(D mid MIM_IO) 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 logic of that adjudication reduces to one ratio. For sequence data compared under a universal-common-ancestry model against an independent-origins model, K=P(D∣MUCA)P(D∣MIO)K = \frac{P(D \mid M_{\text{UCA}})}{P(D \mid M_{\text{IO}})}. and K , the Bayes factor, states exactly how many times more probable the observed data D are under one model than the other - not a correlation coefficient, not a subjective sense of resemblance, but a single number with a precise probabilistic meaning that can in principle come out favouring either model. For the proteins Theobald examined, it was not close. Universal common ancestry came out favoured over the closest competing multiple-ancestry hypothesis by odds reported on the order of ten to the power of two…

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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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