2U: An Exact Interval Propagation Algorithm for Polytrees with Binary Variables

This paper addresses the problem of computing posterior probabilities in a discrete Bayesian network where the conditional distributions of the model belong to convex sets. The computation on a general Bayesian network with convex sets of conditional distributions is formalized as a global optimization problem. It is shown that such a problem can be reduced to a combinatorial problem, suitable to exact algorithmic solutions. An exact propagation algorithm for the updating of a polytree with binary variables is derived. The overall complexity is linear to the size of the network, when the maximum number of parents is fixed. © 1998 Elsevier Science B.V. All rights reserved.