# Bayes' theorem

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Related to Bayesian updating: Bayesian analysis, Bayesian approach

## 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.
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## 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 ?
The posterior PDF of the model parameter is obtained using Bayesian updating, implemented using the MCMC algorithms.
For this special case, the sequential Bayesian updating process on nearest neighbors starts from nearest neighbor [i.sub.1]([u.sub.1]) and ends at nearest neighbor [i.sub.m]([u.sub.m]) in a Markov-type neighborhood around the location [u.sub.0] being estimated (see Figure 1(b) as an example).
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 [??], and (2) q(k) is nonlinear in the prior rating q (k-1), which results in nontrivial reporting strategies even under linear preferences, as we show later.
When Bayesian updating was applied without the uncertainty factor, most of the weight shifted from three modes for [q.sub.net] to predominantly two modes for each net type (Fig.
To facilitate the Bayesian updating, this function will be replaced by a family of functions [F.sub.i](y|[THETA] = [[theta].sub.k]) (k = 1, 2, ..., m), each having equal epistemic weight 1/m (Sec 4.3).
Employers are assumed to use Bayesian updating when forming beliefs about the ability of workers.
If Yolanda, for example, behaves according to this view of adaptation, then she will not follow the Cournot reaction curve or sequential Bayesian updating. On the contrary, if she and Xavier selected outcome 2 in the first period, she will see that she could be better off by moving to row 3 or row 4, and that will be sufficient.
The reputation of i for being the good type is denoted by [p.sup.i.sub.t+1], stemming from Bayesian updating of [p.sup.i.sub.t] after observing outputs in t.
The probability distribution function (pdf) given as g([center dot]) would evidence Bayesian updating if present.
The CM does not have, therefore, a Bayesian updating cost.

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