# Bayes' theorem

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Related to Bayes' rule: Bayes' formula

## Bayes’ theorem

Simplistically, Bayes’ theorem is a formula which allows one to find the probability that an event occurred as the result of a particular previous event. It is often used in medicine to determine the mathematical relationship between the probability that an individual has a disease, X, before the test is run, to the probability that the individual has the disease after the test result is known.

## theorem

(the'o-rem) [Gr. theorema, principle arrived at by speculation]
A proposition that can be proved by use of logic, or by argument, from information previously accepted as being valid.

### Bayes' theorem

See: Bayes' theorem.
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References in periodicals archive ?
For the test trials, the probability that movement regime is m conditioned on activity y in delay can be calculated by Bayes' rule illustrated in (4).
Bayes' rule with Gaussian hypothesis was utilized to estimate the target direction quantitatively.
At the end of the first period, having observed the amount of money demanded (but not the random shock), the central bank updates beliefs about them using Bayes' rule.
These decisions were consistent with Bayes' rule and with private information.
As this announcement does not occur on the equilibrium path, this (admittedly strange) belief does not contradict the assumption that on the equilibrium path beliefs are updated by Bayes' rule. With these beliefs the private sector always expects inflation to be given by the discretionary rule, regardless of announcement.
Further, since [q.sub.a] = [q.sub.b], it is immediate from Bayes' Rule that the posterior belief associated with [S.sub.i] = 1 is simply equal to the prior belief [Pi].
Unless we track the changes in our confidence by using Bayes' rule to update inductive probabilities, all unrefuted hypotheses remain equally trustworthy and equally testworthy.
In order to apply Bayesian analysis to fMRI data and make inference to the parameters that we are interested in, like finding the change points in the dataset, we need to set up a probability model for the data and find a prior to apply Bayes' Rule.
Thus, if an employee goes to her for advice, she must use Bayes' rule to determine the probability that the employee's problem is big or small.

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