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Bayesian inference: the role of coherence to deal with a prior belief function

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Abstract

Starting from a likelihood function and a prior information represented by a belief function, a closed form expression is provided for the lower envelope of the set of all the possible “posterior probabilities” in finite spaces. The same problem, removing the hypothesis of finiteness for the domain of the prior, is then studied in the finitely additive probability framework by considering either the whole set of coherent extensions or the subset of disintegrable extensions.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, University of Perugia, Perugia, Italy

    G. Coletti

  2. Dipartimento di Scienze di Base e Applicate per l’Ingegneria (S.B.A.I.), La Sapienza, University of Rome, Rome, Italy

    D. Petturiti & B. Vantaggi

Authors
  1. G. Coletti
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  2. D. Petturiti
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  3. B. Vantaggi
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Correspondence to B. Vantaggi.

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Coletti, G., Petturiti, D. & Vantaggi, B. Bayesian inference: the role of coherence to deal with a prior belief function. Stat Methods Appl 23, 519–545 (2014). https://doi.org/10.1007/s10260-014-0279-2

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