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

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  • G. Coletti
  • D. Petturiti
  • B. Vantaggi

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. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • G. Coletti & D. Petturiti & B. Vantaggi, 2014. "Bayesian inference: the role of coherence to deal with a prior belief function," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(4), pages 519-545, November.
    • Handle: RePEc:spr:stmapp:v:23:y:2014:i:4:p:519-545
    DOI: 10.1007/s10260-014-0279-2
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    References listed on IDEAS

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    1. Coletti, Giulianella & Gervasi, Osvaldo & Tasso, Sergio & Vantaggi, Barbara, 2012. "Generalized Bayesian inference in a fuzzy context: From theory to a virtual reality application," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 967-980.
    2. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
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    Cited by:

    1. Pierpaolo Angelini, 2020. "A Portfolio of Risky Assets and Its Intrinsic Properties," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 12(3), pages 1-61, June.
    2. Angelini, Pierpaolo & Maturo, Fabrizio, 2022. "The price of risk based on multilinear measures," International Review of Economics & Finance, Elsevier, vol. 81(C), pages 39-57.
    3. Angelini Pierpaolo, 2019. "An Original and Additional Mathematical Model Characterizing a Bayesian Approach to Decision Theory," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 11(3), pages 1-13, June.
    4. Pierpaolo Angelini & Fabrizio Maturo, 2020. "Non-Parametric Probability Distributions Embedded Inside of a Linear Space Provided with a Quadratic Metric," Mathematics, MDPI, vol. 8(11), pages 1-17, October.
    5. Angelini Pierpaolo & Angela De Sanctis, 2019. "An Essential Analogy Between Coherent Previsions of Random Gains and Well-Behaved Preferences," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 8(3), pages 1-46, November.

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