  In this paper we examine the problem of inference in Bayesian Networks with
discrete random variables that have very large or even unbounded domains. For
example, in a domain where we are trying to identify a person, we may have
variables that have as domains, the set of all names, the set of all postal
codes, or the set of all credit card numbers. We cannot just have big tables of
the conditional probabilities, but need compact representations. We provide an
inference algorithm, based on variable elimination, for belief networks
containing both large domain and normal discrete random variables. We use
intensional (i.e., in terms of procedures) and extensional (in terms of listing
the elements) representations of conditional probabilities and of the
intermediate factors.
