Relating epistemic irrelevance to event trees

Abstract

We relate the epistemic irrelevance in Walley's behavioural theory of imprecise probabilities to the event-tree independence due to Shafer. In particular, we show that forward irrelevance is equivalent to event-tree independence in particular event trees, suitably generalised to allow for the fact that imprecise rather than precise probability models are attached to the nodes in the tree. This allows us to argue that in a theory of uncertain processes, the asymmetrical notion of epistemic irrelevance has a more important role to play than its more involved and symmetrical counterpart called epistemic independence. © 2008 Springer-Verlag Berlin Heidelberg.