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Equation 4 · Part 9 · Comparing the Main Approaches to Origins of Life and Astrobiology

Numerator: P(D mid H_bio) P(H_bio)

P(Hbio∣D)=P(D∣Hbio) P(Hbio)P(D∣Hbio) P(Hbio)+P(D∣Hab) P(Hab)P(H_{bio} \mid D) = \frac{P(D \mid H_{bio})\, P(H_{bio})}{P(D \mid H_{bio})\, P(H_{bio}) + P(D \mid H_{ab})\, P(H_{ab})}
P(D∣Hbio) P(Hbio)P(D \mid H_{bio})\, P(H_{bio})

What this part means

The complete quantity above the fraction bar.

Its job in the formula

P(D mid HbH_bio) P(HbH_bio) is one of the signed contributions combined to compute the quantity on the left.

The passage around this formula

What lets these three very different kinds of evidence be compared at all is a shared logical structure that the Astrobiology community has tried to formalize explicitly rather than leave implicit. David Catling and coauthors proposed treating a biosignature detection as a Bayesian inference problem: a prior probability that a given planet or sample harbors life, updated by the likelihood of the observed data under a “life” hypothesis versus under one or more specific abiotic alternative hypotheses, yields a posterior probability rather than a binary yes-or-no verdict [ 7 ] . Written compactly, for a single candidate abiotic alternative HabH_{ab} competing with a life hypothesis HbioH_{bio} given…

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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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