# Definition of *Bayes' theorem* in English:

## Bayes' theorem^{}

### noun

StatisticsA 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.

*‘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.’**‘To summarize the principle of our approach, we used Bayes' theorem to rewrite the posterior pdf as a function of a prior and a likelihood.’**‘The projections of the four individual submodels were integrated into a single prediction based upon Bayes' theorem.’*

**Pronunciation**

**Origin**

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

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