It is well known that the classical Bayesian posterior arises naturally as the unique solution of different optimization problems, without the necessity of interpreting data as conditional probabilities and then using Bayes’ Theorem. Here it is shown that the Bayesian posterior is also the unique minimax optimizer of the loss of self-information in combining the prior and the likelihood distributions, and is the unique proportional consolidation of the same distributions. These results, direct corollaries of recent results about conflations of probability distributions, further reinforce the use of Bayesian posteriors, and may help partially reconcile some of the differences between classical and Bayesian statistics.

Characterization of the Bayesian Posterior Distribution in Terms of Self-information / Dall'Aglio, Marco; Hill Theodore, P.. - In: INTERNATIONAL JOURNAL OF STATISTICS AND PROBABILITY. - ISSN 1927-7032. - 7:1(2018), pp. 21-25. [10.5539/ijsp.v7n1pxx]

Characterization of the Bayesian Posterior Distribution in Terms of Self-information

DALL'AGLIO, MARCO
;
2018

Abstract

It is well known that the classical Bayesian posterior arises naturally as the unique solution of different optimization problems, without the necessity of interpreting data as conditional probabilities and then using Bayes’ Theorem. Here it is shown that the Bayesian posterior is also the unique minimax optimizer of the loss of self-information in combining the prior and the likelihood distributions, and is the unique proportional consolidation of the same distributions. These results, direct corollaries of recent results about conflations of probability distributions, further reinforce the use of Bayesian posteriors, and may help partially reconcile some of the differences between classical and Bayesian statistics.
Bayesian analysis, conflation of probability distributions, likelihood ratio, Shannon information
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11385/176161
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