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Finitely maxitive conditional possibilities, Bayesian-like inference, disintegrability and conglomerability. (English) Zbl 1383.62060
Summary: The aim of the paper is to study Bayesian-like inference processes involving coherent finitely maxitive $$T$$-conditional possibilities assessed on infinite sets of conditional events. Coherence of an assessment consisting of an arbitrary possibilistic prior and an arbitrary possibilistic likelihood function is proved, thus a closed form expression for the envelopes of the relevant joint and posterior possibilities is given when $$T$$ is the minimum or a strict t-norm. The notions of disintegrability and conglomerability are also studied and their relevance in the infinite version of the possibilistic Bayes formula is highlighted.

##### MSC:
 62F15 Bayesian inference 60A05 Axioms; other general questions in probability 62F86 Parametric inference and fuzziness
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