Integrated Likelihood in a Finitely Additive Setting

  • Authors:
  • Giulianella Coletti;Romano Scozzafava;Barbara Vantaggi

  • Affiliations:
  • Università di Perugia, Italy;Università di Roma "La Sapienza", Italy;Università di Roma "La Sapienza", Italy

  • Venue:
  • ECSQARU '09 Proceedings of the 10th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
  • Year:
  • 2009

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Abstract

Without a clear, precise and rigorous mathematical frame, is the likelihood "per se" a proper tool to deal with statistical inference and to manage partial and vague information? Since (as Basu puts it) "the likelihood function is after all a bunch of conditional probabilities", a proper discussion of the various extensions of a likelihood from a point function to a set function is carried out by looking at a conditional probability as a general non-additive "uncertainty" measure P (E | · ) on the set of conditioning events.