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Old 06-04-2007, 10:46 AM
Zeno Zeno is offline
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Join Date: Sep 2002
Location: Spitsbergen
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Default Re: What\'s the probability that Jesus

Some more help: Bayes' Theorem


And this is of some interest:

Bayesian Probability

Note below for an excerpt from the second link -

"Controversy

A quite different interpretation of the term probable has been developed by frequentists. In the "frequency probability" interpretation, what are probable are not propositions entertained by believers, but events considered as members of collectives to which the tools of statistical analysis can be applied.

The Bayesian interpretation of probability allows probabilities to be assigned to all propositions (or, in some formulations, to the events signified by those propositions) in any reference class of events, independent of whether the events can be interpreted as having a relative frequency in repeated trials. Controversially, Bayesian probability assignments are relative to a (possibly hypothetical) rational subject: it is therefore not inconsistent to be able to assign different probabilities to the same proposition by Bayesian methods based on the same observed data. Differences arise either because different models of the data generating process are used or because of different prior probability assignments to model parameters. Differences due to model differences are possible in both Frequentist and Bayesian analyses, but differences due to prior probabilities assignments are distinctive to Bayesian analyses. Such probabilities are sometimes called 'personal probabilities', although there may be no particular individual to whom they belong. Frequentists argue that this makes Bayesian analyses subjective, in the negative sense of 'not determined from the data'. Bayesians typically reply that differences due to alternative models of the data generating process are equally subjective, and that such model choices are also (ideally) chosen prior to analysis of the data, by the analyst. Since the analyst is also a natural person to assign prior probabilities, the two subjective inputs can be seen as deriving from the same source.

Although there is no reason why different interpretations (senses) of a word cannot be used in different contexts, there is a history of antagonism between Bayesians and frequentists, with the latter often rejecting the Bayesian interpretation as ill-grounded. The groups have also disagreed about which of the two senses reflects what is commonly meant by the term 'probable'. More importantly, the groups have agreed that Bayesian and Frequentist analyses answer genuinely different questions, but disagreed about which class of question it is more important to answer in scientific and engineering contexts."

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-Zeno
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