Strong Conditional Independence for Credal Sets

This paper investigates the concept of strong conditional independence for sets of probability measures. Couso, Moral and Walley [7] have studied different possible definitions for unconditional independence in imprecise probabilities. Two of them were considered as more relevant: epistemic independence and strong independence. In this paper, we show that strong independence can have several extensions to the case in which a conditioning to the value of additional variables is considered. We will introduce simple examples in order to make clear their differences. We also give a characterization of strong independence and study the verification of semigraphoid axioms.

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