# 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.

## 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.

## 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).$${\rm Pr(D\vert S) = {Pr(S\vert D) \times Pr(D)\over Pr(S)}$$
References in periodicals archive ?
Because of the independence of the laboratories, using Bayes Theorem with Eqs.
Designed to help readers make the correct choices in the development of clinical research programs, this covers basic probability and the Bayes Theorem, compounding and the law of total probability, intermediate compounding and prior distribution, completing first Bayesian computations, cleaning up when worlds collide, developing prior probability, loss and risk in using posterior distribution, developing the illustration, determining Bayesian sample size, using predictive power and adaptive procedures, and finding out whether the problem is a Bayes problem.
By using the powerful Bayes Theorem, we developed the WinAward solution to help companies correctly evaluate government opportunities and identify those they should bid on, thereby optimizing resources and bid win ratios for the company," said Joanne Damours, Bayesian Systems' president and CEO.
Deadlock avoidance is based on a set of routing rules connected with the maximal values of posterior probabilities computed from the Bayes theorems.

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