# Bayes theorem

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Related to Bayes theorem: conditional probability

## Bayes the·o·rem

(bāyz),the impacts of new data on the evidential merits of competing scientific hypotheses are compared by computing for each the product of the antecedent plausibility (the prior probability) and the likelihood of the current data given that hypothesis (the conditional probability) and rescaling them so that their total is unity (the rescaled values being posterior probabilities).

See also: diagnostic sensitivity, diagnostic specificity, predictive value.

See also: diagnostic sensitivity, diagnostic specificity, predictive value.

## Bayes the·o·rem

(bāyz thē'ŏr-ĕm)A method of calculating statistical probability that combines a prior estimate of probability with statistics derived from subsequent events or experiments. Although it lacks mathematical rigor, it is often used to infer degree of risk in various medical settings.

Synonym(s): bayesian analysis.

Synonym(s): bayesian analysis.

## Bayes,

Thomas, English mathematician, 1702-1761.**Bayes theorem**- to determine the impact of new data on the evidential merits of competing scientific hypotheses.

## Bayes theorem

a statistical means of including local general information, intuitive judgment, clinical skill as learned over a long period, and similar subjective influences, in the assessment of probability, e.g. in making a diagnosis. The formula relates, for example, the conditional probability P(D/S), of a disease (D) being present when a particular sign (S) is observed, to three other probabilities: the prevalence of the disease P(D), the frequency of the sign P(S), and the probability of the sign occurring for the disease P(SD).$${\rm Pr(D\vert S) = {Pr(S\vert D) \times Pr(D)\over Pr(S)}$$

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