# Bayes' theorem

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Related to Bayes formula: conditional probability, Bayes rule

## Bayes' theorem

(beɪz)
n
(Statistics) 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
[C20: named after Thomas Bayes (1702–61), English mathematician and Presbyterian minister]
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 Noun 1 Bayes' theorem - (statistics) a theorem describing how the conditional probability of a set of possible causes for a given observed event can be computed from knowledge of the probability of each cause and the conditional probability of the outcome of each causetheorem - an idea accepted as a demonstrable truthstatistics - a branch of applied mathematics concerned with the collection and interpretation of quantitative data and the use of probability theory to estimate population parameters
References in periodicals archive ?
The objective of the analysis that follows is to show how the statistical Bayes formula (theorem) to update beliefs (5-10) can be used to interpret the TD (PoF) information and to determine if the device (system) of interest is still sound (healthy) or has become faulty, and to use this information to identify a faulty device, if any.
of Hong Kong) introduce inverse Bayes formula (IBF)-based methods for missing data problems which combine the strengths of existing approaches via data augmentation.
The general Bayes formula is never given, so that, even for the mathematically adept student, the formulas used must be memorized as separate cases.

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