Bayes' theorem Line breaks: Bayes' the|orem
Pronunciation: /ˈbeɪz θɪərəm/

# Definition of Bayes' theorem in English:

### noun

Statistics
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.

### Derivatives

#### Bayesian

1
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.

### Origin

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

## Definition of Bayes' theorem in:

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### More words in this category

baseline bivariate central tendency cluster cross-sectional