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Entropy 1999, 1(4), 99-110; doi:10.3390/e1040099

Evidence and Credibility: Full Bayesian Significance Test for Precise Hypotheses

Instituto de Matemática e Estatística, Universidade de São Paulo, 05315-970, Brasil
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Received: 9 February 1999 / Accepted: 9 April 1999 / Published: 25 October 1999
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Abstract

A Bayesian measure of evidence for precise hypotheses is presented. The intention is to give a Bayesian alternative to significance tests or, equivalently, to p-values. In fact, a set is defined in the parameter space and the posterior probability, its credibility, is evaluated. This set is the "Highest Posterior Density Region" that is "tangent" to the set that defines the null hypothesis. Our measure of evidence is the complement of the credibility of the "tangent" region.
Keywords: Bayes factor; numerical integration; global optimization; p-value; posterior density Bayes factor; numerical integration; global optimization; p-value; posterior density
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

De Bragança Pereira, C.A.; Stern, J.M. Evidence and Credibility: Full Bayesian Significance Test for Precise Hypotheses. Entropy 1999, 1, 99-110.

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