Interval Influence Diagrams
  We describe a mechanism for performing probabilistic reasoning in influence
diagrams using interval rather than point valued probabilities. We derive the
procedures for node removal (corresponding to conditional expectation) and arc
reversal (corresponding to Bayesian conditioning) in influence diagrams where
lower bounds on probabilities are stored at each node. The resulting bounds for
the transformed diagram are shown to be optimal within the class of constraints
on probability distributions that can be expressed exclusively as lower bounds
on the component probabilities of the diagram. Sequences of these operations
can be performed to answer probabilistic queries with indeterminacies in the
input and for performing sensitivity analysis on an influence diagram. The
storage requirements and computational complexity of this approach are
comparable to those for point-valued probabilistic inference mechanisms, making
the approach attractive for performing sensitivity analysis and where
probability information is not available. Limited empirical data on an
implementation of the methodology are provided.
