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 | |||||||||
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| 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 |
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| 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 |
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| Date: | 2014 | |||||||||
| Page Range: | pp. 236-254 | |||||||||
| Volume: | 22 | |||||||||
| Number: | 2 | |||||||||
| ISSN: | 1367-0751 | |||||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/21921 |
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