Bayes' theorem


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Related to Bayes' theorem: conditional probability

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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Reference 2 discusses the application of Bayes' Theorem to a horse-racing example.
Applying Bayes' Theorem to clinical trials
Bayes' theorem tells us that the value of a piece of evidence in testing a particular assertion is determined by its likelihood ratio.
Epidemiological uncertainty, causation, and drug product liability
Let's analyze SPOT using Bayes' Theorem and some numerical approximations and conservative assumptions.
Screening tests for terrorism: does the TSA's latest procedure make us safer?
That being the case, Bayes' theorem tells us that when the level of statistical significance is set at P <0.
Bayesian statistics: how to quantify uncertainty
5) Bayes' theorem postulates that the probability of an event E occurrence, conditioned by hypothesis H is proportional to the product of the probability of E by the probability of H conditioned by E or, accordingly, that the probability of E conditioned by H is modified in the same direction and at the same magnitude as the probability of H conditioned by E (see de Finetti (1931a)(1931b)).
On the existence of the true value of a probability. Part 2: the representation
Bayes' Theorem can also be written as Equation 3 below where ([alpha]) consists of the set of (m) parameters of the cumulative (unknown) distribution [PHI]( x | [alpha] ).
A statistical approach to the development of progress plans utilizing Bayesian methods and expert judgment
In general, Bayes' theorem tells us that new information should be interpreted in light of what is already known.
Using the likelihood ratio
When we observe the training data D, we adjust the prior density to a posterior density using Bayes' theorem (level-1 inference).
A comparison of state-of-the-art classification techniques for expert automobile insurance claim fraud detection
In technical terms, Bayes' Theorem states that the subjective posterior odds (odds after being exposed to new data) (32) that a hypothesis is true can be determined by multiplying the prior odds (or odds before exposure to the new data) (33) by the ratio of (1) the probability that the data would have been observed if the hypothesis were true to (2) the probability that the data would have been observed if the hypothesis were not true.
Bayesian approaches to the precautionary principle
Bayes' theorem adds common sense to the maths used to work out how likely something is.
e-business: Probably the best way to assess odds
This articles discusses ways to respond to the need for criterion referenced information using Bayes' theorem, a method coupled with criterion referenced testing in the early 1970s.
Responding to Testing Needs in the Twenty-First Century with an Old Tool
Bayes' Theorem makes it possible to infer the probability of an event by examining past events and new observations, and chaining the probabilities to maximize the amount of learned information that can be applied to a problem.
The Quest for Meaning

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