  Since exact probabilistic inference is intractable in general for large
multiply connected belief nets, approximate methods are required. A promising
approach is to use heuristic search among hypotheses (instantiations of the
network) to find the most probable ones, as in the TopN algorithm. Search is
based on the relative probabilities of hypotheses which are efficient to
compute. Given upper and lower bounds on the relative probability of partial
hypotheses, it is possible to obtain bounds on the absolute probabilities of
hypotheses. Best-first search aimed at reducing the maximum error progressively
narrows the bounds as more hypotheses are examined. Here, qualitative
probabilistic analysis is employed to obtain bounds on the relative probability
of partial hypotheses for the BN20 class of networks networks and a
generalization replacing the noisy OR assumption by negative synergy. The
approach is illustrated by application to a very large belief network, QMR-BN,
which is a reformulation of the Internist-1 system for diagnosis in internal
medicine.
