Arianna Casanova:
Information Algebras in the Theory of Imprecise Probabilities

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This presentation takes up and deepens the compatibility problem; the problem of establishing if some probabilistic assessments have a common joint probabilistic model, in the framework of desirability. In particular, we prove the possibility to induce information algebras from coherent sets of gambles and coherent lower previsions, both interpreted as pieces of information about values of a group of variables. Then, we show that it is possible to obtain the same results of Miranda and Zaffalon (2020) about the compatibility problem in the unconditional case in a more simple way by using only instruments of these general algebraic structures. This allows us moreover to enforce the view of such imprecise-probability objects as algebraic and logical structures and gives tools to manipulate them as such.

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Arianna Casanova started her Ph.D. at Dalle Molle Institute for Artificial Intelligence (IDSIA) in May 2018. Previously, she received a BSc and an MSc degree in mathematics both from the University of Milan. Her work focuses on the analysis and generalisation of the imprecise-probability formalism of desirability.