# 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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In both treatments, the estimated cutoff rule was consistent with Bayes' Rule when the prior was 1/3 and 2/3.
Maximum likelihood estimation of the decision rules used by subjects not allowed to purchase insurance (separated by treatment depending on whether they observed prices) found that for priors closer to one-half, Bayes' Rule provided a good fit.
27 TABLE 2 Predicted Cut-Points Cut-Point for Cut-Point for Cut-Point for Pr(A) = 1/3 Pr(A) = 2/3 Pr(A) = 5/6 Bayes' Rule 4 2 1 Representative 3 3 2,3 Conservative 5,6 -1,0,1 -1,0 Note: A cut-point specifies that Cup A is chosen if the number of orange balls drawn is greater than the specified number for a given prior.
Under the assumption that people use Bayes' rule to form posterior probabilities, previous public decisions are less informative when the possibility of decision error is higher.
These decisions were consistent with Bayes' rule and with private information.
157) The empirical estimates of the parameters underlying Bayes' rule are just those kinds of facts upon which statistical experts would rely in forming an opinion as to the posterior source probability.
This is asking jurors to rediscover Bayes' rule without any help.
Again, beliefs at the SP information set satisfy Bayes' rule, and the supervisors' actions are rational there.
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.
But appropriate application of Bayes' rule, far from preempting the
our notation and model applying Bayes' rule and explains why the

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