# Bayes' theorem

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## 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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Bayesian network probabilistic graphical models have been widely used to solve various problems (for example diagnosis, failure prediction and risk analysis, classification) [4].
The accuracy of the Bayesian stepwise discriminant model was validated by both a training group (including 112 cases in case subgroup and 108 cases in control subgroup) and a multicenter validation group (including 500 cases in case subgroup and 500 cases in control subgroup).
This paper focuses on volatility modeling of the JSE all share index and risk estimation using the Bayesian and frequentist approaches.
In the end, PPD and/or other Bayesian forecasting has the potential to achieve stable drug concentrations more quickly, maximize patient care, reduce treatment complications and expenses, shorten the duration of postoperative hospitalization, and improve transplantation success rates.
Bayesian networks (BNs) is one of the approaches found in MCDM which has the ability to tackle the uncertainties (Watthayu, 2009).
On the other hand, Bayesian inference often costs more computationally and requires at least one of elicitation of real subjective probability distributions of prior beliefs.
In other articles Bayesian network and ANP calibration methods combined as a new assessment method have not been used.
In Bayesian analysis the comparisons among different estimators are made on the basis of loss functions.
This example is not nearly as large or complex as many medical trials but still was addressed through the Bayesian inference using the Gibbs sampling (BUGS) computer program initially developed by the Medical Research Council Biostatistics Unit in Cambridge, U.
In this letter we use only first order derivative constraint with the Bayesian beamformer to fix the binning error.

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