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Published equation contexts

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

Why this formula appears here

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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DD

Symbol D

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.

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MUCAM_{\text{UCA}}

Symbol M_UCA

MUM_UCA occurs above the fraction bar. The numerator is divided by the entire denominator below it.

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MIOM_{\text{IO}}

Symbol M_IO

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

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P(D∣MIO)P(D \mid M_{\text{IO}})

Denominator: P(D mid M_IO)

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

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How to interpret it

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)

A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.

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

Equation 1 · Evolutionary Biology

One Tree: The Statistics of Common Descent

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

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…

Meanings in this article

  • DD: 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.
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