Structural Uncertainty in Belief Nets

The project suggests a new framework for analyzing the uncertainty over the graphical structure of belief nets (Bayes nets). The basic idea is to introduce a probability function on the family of all possible orderings (representable as a convex polyhedron) of the variables of a given problem. In the resulting probability space the probabilities of negations, of conjunctions or of disjunctions of structures can be derived. The main theoretical goal of the project is to justify the structural uncertainties statistically by the data from which the Bayes net is learned. The main practical goal is to employ the new framework for the assessment of belief nets from experts. For someone not familiar with Bayes nets the qualitative part of a belief net is much easier to understand than its quantitative part containing a set of multidimensional probability tables. Structural uncertainties provide a well defined semantic that is helpful to start the assessment with the qualitative part of the network.