Bayesian network inference with qualitative expert knowledge for group decision making

In this paper, we propose a practical framework and a methodology for transforming final group decision making statements or expert knowledge into a set of qualitative statements and probability inequality constraints for inference in a Bayesian Network. First we present several techniques in the decision process to produce a group preference ranking and a final group solution. Second, we describe a detailed method to transform the final group solution into a set of qualitative statements and an “a priori” distribution for Bayesian probabilistic models. The decision-making assumptions and the mathematical equation for Bayesian inference are derived based on data and knowledge obtained from experts. We also propose a simplified method for constructing the “a priori” model distribution. Each statement obtained from the group´s solution is used to constrain the model space to the subspace which is consistent with the statement provided. Finally, we present qualitative knowledge models and then show a full formalism of how to translate a set of qualitative statements into probability inequality constraints.