Summary: Equivalence between Bayesian and Credal Nets
on an Updating Problem
Alessandro Antonucci and Marco Zaffalon
Istituto Dalle Molle di Studi sull'Intelligenza Artificiale (IDSIA)
Galleria 2, CH-6928 Manno (Lugano), Switzerland
We establish an intimate connection between Bayesian and credal nets.
Bayesian nets are precise graphical models, credal nets extend Bayesian nets
to imprecise probability. We focus on traditional belief updating with credal
nets, and on the kind of belief updating that arises with Bayesian nets when
the reason for the missingness of some of the unobserved variables in the net
is unknown. We show that the two updating problems are formally the same.
Imagine the following situation. You want to use a graphical model to formal-
ize your uncertainty about a domain. You prefer precise probabilistic models
and so you choose the Bayesian network (BN) formalism  (see Sect. 2.1).
You take care to precisely specify the graph and all the conditional mass
functions required. At this point you are done with the modelling phase, and
start updating beliefs about a target variable conditional on the observation
of some variables in the net. The remaining variables are not observed, i.e.,