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Bayesian epistemic values: focus on surprise, measure probability!

Stern, Julio Michael and De Braganca Pereira, Carlos Alberto (2014) Bayesian epistemic values: focus on surprise, measure probability! [Preprint]

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Abstract

The e-value or epistemic value, ev(H), measures the statistical significance of H, a hypothesis about the parameter θ of a Bayesian model. The e-value is obtained by a probability-possibility transformation of the model’s posterior measure, p(θ), and can, in turn, be used to define the FBST or Full Bayesian Significance Test. This article investigates the relation of this novel approach to more standard probability-possibility transformations. In particular, we show how and why the e-value focus on or conforms with s(θ)=p(θ)/r(θ), the model's surprise function relative to the reference density r(θ), while it keeps itself consistent with the model’s posterior probability measure. In addition, we investigate traditional objections raised in decision theoretic Bayesian statistics against measures of significance engendered by probability-possibility transformations.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Stern, Julio Michael0000-0003-2720-3871
De Braganca Pereira, Carlos Alberto
Additional Information: Compiled from the author's preprint LaTeX file
Keywords: Bayesian models, Belief calculi transformations, Complex hypotheses, Epistemic values, Possibilistic and probabilistic reasoning, Significance tests, Surprise function, Truth function.
Subjects: General Issues > Confirmation/Induction
General Issues > Evidence
General Issues > Laws of Nature
Specific Sciences > Probability/Statistics
Depositing User: Prof. Julio Michael Stern
Date Deposited: 31 Mar 2023 12:30
Last Modified: 31 Mar 2023 12:30
Item ID: 21921
Journal or Publication Title: Logic Journal of IGPL
Official URL: http://doi.org/10.1093/jigpal/jzt023
DOI or Unique Handle: 10.1093/jigpal/jzt023
Subjects: General Issues > Confirmation/Induction
General Issues > Evidence
General Issues > Laws of Nature
Specific Sciences > Probability/Statistics
Date: 2014
Page Range: pp. 236-254
Volume: 22
Number: 2
ISSN: 1367-0751
URI: http://philsci-archive.pitt.edu/id/eprint/21921

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