# Bayes' theorem

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## 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]
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
References in periodicals archive ?
The theory that would not die: how Bayes' rule cracked the enigma code, hunted down Russian submarines and emerged triumphant from two centuries of controversy.
Bayesian inference is a method of statistical inference in which Bayes' Rule is applied to update the probability estimate for a hypothesis as evidence is acquired, and it is the formal method for combining prior beliefs with observed (quantitative) information to answer the questions that researchers are usually interested in like "what is the probability of getting lung cancer for certain patients who smoke one pack per day?
He covers the basics: models, probability, Bayes' rule, and R; all the fundamentals applied to inferring a binomial probability; and the generalized linear model.
Bayes' rule implies that the belief at period t + [DELTA] is given by
Chapters then cover basic terms of probability, relationships between two events, probability rules, Bayes' rule in particular, and measurement of uncertainty.
McGrayne, "The Theory That Would Not Die: How Bayes' Rule Cracked The Enigma Code, Hunted Down Russian Submarines, & Emerged Triumphant from Two Centuries of Controversy," New Haven: Yale University Press, 2011.
We are offered the standard fare such as hypothesis testing, experimental design, regression and Bayes' Rule but in such a way as to avoid the usual pedantic and unimaginative (read boring) approach that many books take.
In its simplest form, Bayes' rule (for the case of two hypotheses) states that, when we are trying to discover which of two mutually exclusive and exhaustive hypotheses (H, ~H) are true, we perform an experiment and/or otherwise gather evidence.
Another strand of the literature looks at central bankers that learn using Bayes' rule.
The standard Bayesian approach now tries to specify the hyperparameters [theta] (for the mean of [beta]) and [LAMBDA] (for the variance-covariance matrix of [beta]) and use Bayes' rule for estimation.

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