Improving Construction of Conditional Probability Tables for Ranked Nodes in Bayesian Networks

This paper elaborates on the ranked nodes method (RNM) that is used for constructing conditional probability tables (CPTs) for Bayesian networks consisting of a class of nodes called ranked nodes. Such nodes typically represent continuous quantities that lack well-established interval scales and are hence expressed by ordinal scales. Based on expert elicitation, the CPT of a child node is generated in RNM by aggregating weighted states of parent nodes with a weight expression. RNM is also applied to nodes that are expressed by interval scales. However, the use of the method in this way may be ineffective due to challenges which are not addressed in the existing literature but are demonstrated through an illustrative example in this paper. To overcome the challenges, the paper introduces a novel approach that facilitates the use of RNM. It consists of guidelines concerning the discretization of the interval scales into ordinal ones and the determination of a weight expression and weights based on assessments of the expert about the mode of the child node. The determination is premised on interpretations and feasibility conditions of the weights derived in the paper. The utilization of the approach is demonstrated with the illustrative example throughout the paper.