# Bayes' theorem

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Related to Bayes' theorem: conditional probability

## 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 ?
Naive Bayes based on Bayes' theorem is a popular algorithm in the classification with a machine learning technique.
Combining the prior distribution (8) with the likelihood function (6), the posterior density of [theta] can be derived as follows by using Bayes' theorem,
However, many trainees and caregivers struggle with the application of Bayes' theorem in clinical practice, suggesting a longstanding educational gap that can negatively impact medical decision-making and patient care.
The probabilistic model of naive Bayes classifiers is based on Bayes' theorem, and the adjective naive comes from the assumption that the features in a dataset are mutually independent.
Interpreting the external world in this way can be described precisely (and therefore can be tested and explored in a rigorous way) with the use of a mathematical expression known as Bayes' theorem.
The chapter on probabilistic reasoning starts off well with a brief but informative discussion of Bayes' theorem, but does not pursue this very interesting subject or bring out its more curious aspects.
The Naive Bayes classifier is based on Bayes' Theorem regarding dependent probabilities, which states that
Pastor Thomas Bayes (1702-1761) appears to have had little influence on mathematics outside of statistics where Bayes' Theorem has found wide application.
A naive Bayes classifier is a simple probabilistic classifier based on the application of Bayes' theorem with strong (naive) independence assumptions.
Abstract: Bayes' theorem to the rescue--why I hated stats before the revolution.
Part IF therefore concludes with an examination of such statistical refining methods in determining specific causation in medicinal product liability cases, including the use of Bayes' theorem to help us understand how statistical risks can be refined using personal risk factors.
They describe how to be thorough when thinking about the possible causes of a patient's problem, estimate the probability of a disease, use Bayes' theorem to estimate the post-test probability of a disease, select diagnostic tests using the treatment-threshold probability, measure a patient's attitudes towards risks and benefits of a treatment, and choose among several risky treatment alternatives.

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