Portraying probabilistic relationships of continuous nodes in Bayesian networks with ranked nodes method

Abstract

This paper advances the use of the ranked nodes method (RNM) to portray probabilistic relationships of continuous quantities in Bayesian networks (BNs). In RNM, continuous quantities are represented by ranked nodes with discrete ordinal scales. The probabilistic relationships of the nodes are quantified in conditional probability tables (CPTs) generated with expert-elicited parameters. When ranked nodes are formed by discretizing continuous scales, ignorance about the functioning of RNM can lead to discretizations that make the generation of sensible CPTs impossible. While a guideline exists on this matter, it is limited by a requirement to define an equal number of ordinal states for all the nodes. This paper presents two novel discretization approaches that consider the functioning of RNM and allow the nodes to have non-equal numbers of ordinal states. In the first one, called the “static discretization approach”, the nodes can be given any desired discretizations that stay unchanged during the use of the BN. In the second one, called the “dynamic discretization approach”, the discretizations are algorithmically updated during the use of the BN to help manage the sizes of the generated CPTs. Both approaches are based on the original idea that, besides the RNM parameters, the nodes probabilistic relationship is defined by initial RNM-compatible discretizations elicited from the domain expert. Overall, the new approaches offer an easier and more versatile way of using RNM to depict the probabilistic relationships of continuous quantities. In doing so, they also facilitate the effective and diverse use of BNs in decision support systems.