Bayes' theorem

American  

[beyz, bey-ziz] / beɪz, ˈbeɪ zɪz /

noun

Statistics.

1. a theorem describing how the conditional probability of each of a set of possible causes, given an observed outcome, can be computed from knowledge of the probability of each cause and of the conditional probability of the outcome, given each cause.

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Bayes' theorem British  

/ beɪz /

noun

1. statistics the fundamental result which expresses the conditional probability P ( E/A ) of an event E given an event A as P ( A/E ). P ( E ) /P ( A ); more generally, where En is one of a set of values Ei which partition the sample space, P ( En/A ) = P ( A/En ) P ( En ) / Σ P ( A/Ei ) P ( Ei ). This enables prior estimates of probability to be continually revised in the light of observations

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Etymology

Origin of Bayes' theorem

see origin at Bayesian

Example Sentences

In Bayes’ theorem, “priors” are initial predictions about an event, which we update as new information becomes available.

From The Wall Street Journal • May 16, 2026

Plugging these values into Bayes' theorem, we get:

From Salon • Apr. 30, 2023

“They are basically just hippies who talk a lot more about Bayes’ theorem than the original hippies,” said Scott Aaronson, a University of Texas professor who has stayed in one of the group houses.

From New York Times • Feb. 13, 2021

The formal way to traverse the gap between these two questions is Bayes’ theorem.

From Slate • Jun. 5, 2013

An interesting elaboration on the concept of conditional probability is known as Bayes’ theorem, first proved by Thomas Bayes in the eighteenth century.

From "Innumeracy: Mathematical Illiteracy and Its Consequences" by John Allen Paulos