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Bayes' theorem Syllabification: Bayes' the·o·rem
Pronunciation: /ˈbāz ˌTHēərəm/

Definition of Bayes' theorem in English:

A theorem describing how the conditional probability of each of a set of possible causes for a given observed outcome can be computed from knowledge of the probability of each cause and the conditional probability of the outcome of each cause.
Example sentences
  • Following Bayes' theorem, the posterior distribution over the parameter space is proportional to the likelihood times the prior distribution.
  • A follower of Clifford might object if there was no philosophical discussion of rival explanations or of the application here of Bayes' theorem in the theory of probability.
  • Once these parameters have been estimated, Bayes' theorem is used to estimate the posterior probability that a given site came from the class of positively selected sites.


Pronunciation: /ˈbāzēən/
Example sentences
  • He introduced Bayesian hypothesis tests and Bayesian estimation.
  • We propose a new method for approximate Bayesian statistical inference on the basis of summary statistics.
  • From these Jaynes derives all of the Bayesian machinery for statistical inference.


Mid 19th century: named after Thomas Bayes (1702–61), English mathematician.

Definition of Bayes' theorem in:
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