An expert system for coherent assessment of probabilities in multigraph models

Abstract

In this paper, we present a method that allows a coherent assessment of probabilistic Bayesian networks over sets of nodes or variables that share a common subset. We motivate and illustrate the models with a diseases-symptoms knowledge base defined by multiple Bayesian networks. Since the parameter values for the joint probability distribution of diseases and symptoms must satisfy some compatibility conditions, the probability assessment becomes complicated and can be monitored by an expert system, in order to maintain coherence in the knowledge base. The bases of this expert system are presented. Once the human expert selects one parameter in the model to be assessed, the expert system calculates and provides the human expert with a range of feasible values of the parameter. Any value of the parameter within this range is coherent with the probability axioms. Then, the human expert can specify either a single value or an interval for that parameter in the feasible range. Accordingly, the expert system then updates the feasible ranges for all other parameters. The process can be repeated until all the parameters have been specified. At the end, the expert system gives a final set of values or intervals for all parameters. We apply the proposed system to the dependent-symptoms and the independent-symptoms probabilistic models. We give two numerical examples to illustrate the method. © 1999 John Wiley & Sons, Inc. Networks 33: 193–206, 1999