# Bayes' theorem

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Related to Bayes' rule: Bayes' formula

## Bayes' theorem

[¦bāz ′thir·əm]
(mathematics)
A theorem stating that the probability of a hypothesis, given the original data and some new data, is proportional to the probability of the hypothesis, given the original data only, and the probability of the new data, given the original data and the hypothesis. Also known as inverse probability principle.
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But appropriate application of Bayes' rule, far from preempting the
our notation and model applying Bayes' rule and explains why the
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.
t] and updates beliefs about the parameters of supply using Bayes' rule.
We are interested in whether decisions are more consistent with Bayes' Rule when subjects are given the option to purchase insurance.
We began with the procedures used by Grether (1980) and El-Carnal and Grether (1995) in which subjects guessed from which cup a sample was drawn, and could maximize expected earnings by making decisions in accordance with Bayes' Rule.
Decisions that are consistent with private information but inconsistent with Bayes' rule are labeled * mistakes.
t] giving the private sectors, beliefs about the type of the government is derived whenever possible by Bayes' rule from the prior [Mu] and the government's strategy.
Just as in the determination of i's sincere voting strategy, we can compute via Bayes' Rule the probability that the true state is either A or B - and hence the expected utility from alternative A or B being chosen, conditional on the vector s:
Indeed, Bayes' rule is the only consistent way to mirror them.
In particular, a central claim of this Article is that the appropriate application of Bayes' rule as laid out in equation (7) can lead courts and litigants to focus more explicitly on two variables that have to date been omitted from the adversarial process: a, the probability that nonsources in the database will have an alibi, and p, the prior probability that the source is in the database.
This is consistent with Bayes' rule and also makes the supervisor's mixing at her information set rational.

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