The classical Bayesian posterior arises naturally as the unique solution of several different optimization problems, without the necessity of interpreting data as conditional probabilities and then using Bayes' Theorem. For example, the classical Bayesian posterior is the unique posterior that minimizes the loss of Shannon information in combining the prior and the likelihood distributions. These results, direct corollaries of recent results about conflations of probability distributions, reinforce the use of Bayesian posteriors, and may help partially reconcile some of the differences between classical and Bayesian statistics.

Bayesian Posteriors Without Bayes' Theorem / Dall'Aglio, Marco; Theodore P., Hill. - 1203.0251:(2012).

Bayesian Posteriors Without Bayes' Theorem

DALL'AGLIO, MARCO;
2012

Abstract

The classical Bayesian posterior arises naturally as the unique solution of several different optimization problems, without the necessity of interpreting data as conditional probabilities and then using Bayes' Theorem. For example, the classical Bayesian posterior is the unique posterior that minimizes the loss of Shannon information in combining the prior and the likelihood distributions. These results, direct corollaries of recent results about conflations of probability distributions, reinforce the use of Bayesian posteriors, and may help partially reconcile some of the differences between classical and Bayesian statistics.
Bayesian Posteriors Without Bayes' Theorem / Dall'Aglio, Marco; Theodore P., Hill. - 1203.0251:(2012).
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11385/56256
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