11 Facts About Bayesian probability


Bayesian probability is an interpretation of the concept of probability, in which, instead of frequency or propensity of some phenomenon, probability is interpreted as reasonable expectation representing a state of knowledge or as quantification of a personal belief.

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Bayesian interpretation of probability can be seen as an extension of propositional logic that enables reasoning with hypotheses; that is, with propositions whose truth or falsity is unknown.

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Bayesian probability belongs to the category of evidential probabilities; to evaluate the probability of a hypothesis, the Bayesian probabilist specifies a prior probability.

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The Bayesian probability interpretation provides a standard set of procedures and formulae to perform this calculation.

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Term Bayesian probability derives from the 18th-century mathematician and theologian Thomas Bayes, who provided the first mathematical treatment of a non-trivial problem of statistical data analysis using what is known as Bayesian probability inference.

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Ian Hacking

Bayesian probability methods are characterized by concepts and procedures as follows:.

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The objective and subjective variants of Bayesian probability differ mainly in their interpretation and construction of the prior probability.

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Term Bayesian probability derives from Thomas Bayes, who proved a special case of what is called Bayes' theorem in a paper titled "An Essay towards solving a Problem in the Doctrine of Chances".

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Richard T Cox showed that Bayesian updating follows from several axioms, including two functional equations and a hypothesis of differentiability.

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However, Ian Hacking noted that traditional Dutch book arguments did not specify Bayesian probability updating: they left open the possibility that non-Bayesian probability updating rules could avoid Dutch books.

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The additional hypotheses sufficient to specify Bayesian probability updating are substantial and not universally seen as satisfactory.

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