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Jasper De Bock, Gert de Cooman


Credal networks under epistemic irrelevance using sets of desirable gambles

Abstract

We present a new approach to credal networks, which are graphical models that generalise Bayesian nets to deal with imprecise probabilities. Instead of applying the commonly used notion of strong independence, we replace it by the weaker notion of epistemic irrelevance. We show how assessments of epistemic irrelevance allow us to construct a global model out of given local uncertainty models, leading to an intuitive expression for the so-called irrelevant natural extension of a network. In contrast with Cozman (2000), who introduced this notion in terms of credal sets, our main results are presented using the language of sets of desirable gambles. This has allowed us to derive a number of useful properties of the irrelevant natural extension. It has powerful marginalisation properties and satisfies all graphoid properties but symmetry, both in their direct and reverse forms.

Keywords

credal networks, epistemic irrelevance, sets of desirable gambles, graphoid properties, irrelevant natural extension, lower previsions, coherence


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E-mail addresses

Jasper De Bock   jasper.debock@ugent.be
Gert de Cooman  gert.decooman@ugent.be

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