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.
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Coletti, G., Scozzafava, R., Vantaggi, B. (2009). Integrated Likelihood in a Finitely Additive Setting. In: Sossai, C., Chemello, G. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2009. Lecture Notes in Computer Science(), vol 5590. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02906-6_48
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