# 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 ?
The risk of using temperatures alone as a measure of thermal comfort was quantified by using Bayes' Theorem and calculating probabilities for discomfort from the sample set generated for the sensitivity analysis.
The United Kingdom-based prospective multicenter study, involving 16,747 singleton pregnancies, also looked at the effectiveness of a screening method that used Bayes' theorem to combine maternal risk factors with biomarkers.
The most important fact about conditional probabilities is undoubtedly Bayes' Theorem, whose significance was first appreciated by the British cleric Thomas Bayes in his posthumously published masterwork, "An Essay Toward Solving a Problem in the Doctrine of Chances" (Bayes 1764).
NB is based on Bayes' theorem. In its simplest form, NB assumes that the occurrence or absence of a feature is independent of the value of any other feature given for classification.
Naive Bayes based on Bayes' theorem is a popular algorithm in the classification with a machine learning technique.
Under those assumptions, the Prior Odds necessary to convict a defendant based on his confession must be at least 1, according the equation mentioned above (Bayes' Theorem in an odds form), meaning P(G) [greater than or equal to] P(I).
Thus, by Bayes' theorem the posterior distribution of the parameters of interest is given by
Based on the prior knowledge of Bayes' theorem, the system uses the probability to denote the relation between disease and symptom.
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.

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