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

Bayesian

Example Sentences

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

The most widely accepted method of incorporating knowledge for probability assessment is Bayes' theorem.

From Nature

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

From The Guardian

Part 4 recognizes that Bayes' theorem can be used to solve the problem, no doubt based on the fact that, in its training data, Bayes' theorem is often used to solve these kinds of problems.

From Salon

Plugging these values into Bayes' theorem, we get:

From Salon