# Bayes' theorem

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Related to Bayes' formula: 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]
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014
ThesaurusAntonymsRelated WordsSynonymsLegend:
 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
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References in periodicals archive ?
By combining probabilities that come from prior evidence and current observations, Bayes' formula can be used to calculate an overall estimate of the likelihood that a given suspicion is true.
Using Bayes' formula, and assuming that Pr([p.sub.i]) = Pr([p.sub.j]) for i, j = 1, 2, ..., n, we have the following decision rule based on the likelihood that Pr(r|[p.sub.i]) is the probability that the signal vector r is received, given that the mobile node is located in location [p.sub.i]:

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