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.
References in periodicals archive ?
Afterwards, a new fatigue crack growth prediction approach was proposed based on the prior distribution, in-service observation, and Bayesian updating method.
This sequential Bayesian updating process on nearest neighbors starts from nearest neighbor [i.sub.2]([u.sub.2]) and ends at nearest neighbor [i.sub.m]([u.sub.m]) in a Markov-type neighborhood around the uninformed location [u.sub.0] being estimated (see Figure 1(a) as an example).
Consider the case where the market determines the transaction price according to the Bayesian updating rule.
The Dutch system, in particular, incorporates a complicated bonus-malus class structure that can be viewed as a proxy for a Bayesian updating mechanism.
When equal weighting was applied to the inputs from the different captains without Bayesian updating and without the uncertainty factor, the [q.sub.net] distributions for each net were multimodal (Fig.
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.
Bayesian updating is an alternative general framework in which to understand choices in decentralized games.
On the other hand, choosing a partner with higher reputation than one's own will persuade an entity engaged in Bayesian updating to attribute responsibility for good results more to the other, while bad results are more blamed on oneself.
Agents in the model observe money growth that contains monetary control errors and use Bayesian updating of their beliefs about money growth and the monetary regime that is in place.
Two data sets are estimated using the standard DB-DC format modified to reveal the presence of Bayesian updating. The estimates are compared with a single valuation question (the dichotomous choice [DC-CV])(2) and a standard DB-DC format.
Indeed, the addition of such propositions turns out to be very fruitful, for suitably diagonalizing on them displays unsuspected in-principle limitations on our ability to follow traditional Bayesian updating rules, as the example in the next paragraph shows (see also Howson [1996]).