Bayes' theorem

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P(A \mid B) = \frac{P(B \mid A)\, P(A)}{P(B)}

Flips a conditional probability around: it converts what you would expect to see given a hypothesis into how much the thing you saw should move your belief in it. Every probabilistic update in machine learning is a version of this.

Symbols

$P(A \mid B)$: The posterior — belief in A after seeing B.
$P(B \mid A)$: The likelihood — how expected B was under A.
$P(A)$: The prior — belief in A beforehand.
$P(B)$: The evidence, which normalises the result.

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Bayes' theorem

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