Bayes' theorem

American  

[bayz, bay-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

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Example Sentences

See Examples For:

Bayes' theorem

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

Using Bayes' theorem, the probability that the other side of the card is green, given that we know one side is red, is:

From Salon ● Apr. 30, 2023

Mathematically, this is a consequence of Bayes’ theorem.

From New York Times ● Jan. 8, 2022

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

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