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

Plugging these values into Bayes' theorem, we get:

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

Such is the philosophical – or even "theological" – dispute at the heart of this book on the long controversy over Bayes' theorem.

From The Guardian • Aug. 5, 2011

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