Bayes' theorem

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Alternative forms[edit]


Named after English mathematician Thomas Bayes (1701–1761), who developed an early formulation. The modern expression of the theorem is due to Pierre-Simon Laplace, who extended Bayes' work but was apparently unaware of it.

Proper noun[edit]

Bayes' theorem

  1. (probability theory) A theorem expressed as an equation that describes the conditional probability of an event or state given prior knowledge of another event.
    • 2010, Jonathan Harrington, Phonetic Analysis of Speech Corpora, page 327,
      The starting point for many techniques in probabilistic classification is Bayes' theorem, which provides a way of relating evidence to a hypothesis.
    • 2011, Allen Downey, Think Stats, O'Reilly, page 56,
      Bayes's theorem is a relationship between the conditional probabilities of two events.
    • 2013, Norman Fenton, Martin Neil, Risk Assessment and Decision Analysis with Bayesian Networks, Taylor & Francis (CRC Press), page 131,
      We have now seen how Bayes' theorem enables us to correctly update a prior probability for some unknown event when we see evidence about the event.

Usage notes[edit]

The theorem is stated mathematically as:


where and are events with , and

  • and are the marginal probabilities of observing and without regard to each other.
  • The conditional probability is the probability of observing event given that is true.
  • Similarly, is the probability of observing event given that is true.


Related terms[edit]

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