Bayes' theorem

Bayes' theorem is a result in probability theory. It yields the conditional probability distribution of a random variable A, assuming we know:

Related Topics:
Probability theory - Conditional - Probability distribution - Random variable

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• information about another variable B in terms of the conditional probability distribution of B given A, and
• the marginal probability distribution of A alone.

This article gives a formal mathematical discussion of the theorem, some of its extensions, and an example of its use. As a formal theorem, it is valid regardless of how one interprets probability. However, frequentist and Bayesian interpretations disagree about the kinds of variables with which the theorem can be validly used for statistical inference —the articles on Bayesian probability and frequentist probability discuss these debates at greater length.

Related Topics:
Example - Theorem - Probability - Frequentist - Bayesian - Statistical inference - Frequentist probability

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Bayes' theorem: Historical remarks ►