The e-value and the Full Bayesian Significance Test: Logical Properties and Philosophical Consequences

Julio Michael Stern; Carlos Alberto de Braganca Pereira; Marcelo de Souza Lauretto; Luis Gustavo Esteves; Rafael Izbicki; Rafael Bassi Stern; Marcio Alves Diniz; Wagner de Souza Borges

arXiv · 2205.08010

The e-value and the Full Bayesian Significance Test: Logical Properties and Philosophical Consequences

Julio Michael Stern·Carlos Alberto de Braganca Pereira·Marcelo de Souza Lauretto·Luis Gustavo Esteves·Rafael Izbicki·Rafael Bassi Stern·Marcio Alves Diniz·Wagner de Souza Borges

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Abstract

This article gives a conceptual review of the e-value, ev(H|X) -- the epistemic value of hypothesis H given observations X. This statistical significance measure was developed in order to allow logically coherent and consistent tests of hypotheses, including sharp or precise hypotheses, via the Full Bayesian Significance Test (FBST). Arguments of analysis allow a full characterization of this statistical test by its logical or compositional properties, showing a mutual complementarity between results of mathematical statistics and the logical desiderata lying at the foundations of this theory.

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Julio Michael Stern, Carlos Alberto de Braganca Pereira, Marcelo de Souza Lauretto, Luis Gustavo Esteves, Rafael Izbicki, Rafael Bassi Stern, Marcio Alves Diniz, Wagner de Souza Borges. 2022-05-16. The e-value and the Full Bayesian Significance Test: Logical Properties and Philosophical Consequences. https://arxiv.org/abs/2205.08010

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