# Bayes' theorem

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Related to Bayesian updating: Bayesian analysis, Bayesian approach

## 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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However, as a voter's own final ranks could be flawed, updating toward them maximally "quickly" is just a necessary, and not a sufficient, condition for Bayesian updating.
In Section IV, after first showing evidence of the validity of the estimated posteriors, I use ordinary least squares regressions to test the null hypothesis of Bayesian updating.
When it is assumed that the aftermarket trading price follows a Bayesian updating process, this study shows that underpricing has both positive and negative impacts on the entrepreneur's final wealth.
We choose classical Bayesian updating because (1) the resulting q(k) is the vector of conditional probabilities for the buyer type given the reporting strategy [?
This Bayesian updating is crucial in our two-period model, since in the second period, the buyer has no incentive to underreport.
When Bayesian updating was applied without the uncertainty factor, most of the weight shifted from three modes for [q.
In order to motivate our experiment, we discuss a model based on Farmer and Terrell (1996) and Lewis and Terrell (2001), who examine a statistical discrimination framework with Bayesian updating of employers' beliefs.
The probability distribution function (pdf) given as g([center dot]) would evidence Bayesian updating if present.
This article describes an experiment that introduces a simple insurance option into El-Gamal and Grether's (1995) test of Bayesian updating.
This suggests that deviations from the belief learning pattern can be attributed to imperfect Bayesian updating and not to sophisticated strategic reasoning.
Bayesian updating, and not the Humean principle of induction, is the basic mode of 'learning from experience'.

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