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Bayes' Theorem

Updated 01 Oct 2026

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What it is
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  updates a hypothesis probability using observed evidence
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Formula
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  $P(H\mid E)=P(E\mid H)P(H)/P(E)$ for $P(E)>0$ .
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  for an exhaustive, mutually exclusive set of hypotheses, $P(E)=\sum_iP(E\mid H_i)P(H_i)$ .
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Interpretation
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  prior: $P(H)$ ; likelihood: $P(E\mid H)$ ; posterior: $P(H\mid E)$ .
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  $P(H\mid E)$ and $P(E\mid H)$ are generally different.
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Related
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  Unavailable reference
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  Unavailable reference

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