How to model mutually exclusive events based on independent causal pathways in Bayesian network models

We show that existing Bayesian network (BN) modelling techniques cannot capture the correct intuitive reasoning in the important case when a set of mutually exclusive events need to be modelled as separate nodes instead of states of a single node. A previously proposed 'solution', which introduces a simple constraint node that enforces mutual exclusivity, fails to preserve the prior probabilities of the events, while other proposed solutions involve major changes to the original model. We provide a novel and simple solution to this problem that works in all cases where the mutually exclusive nodes have no common ancestors. Our solution uses a special type of constraint and auxiliary node together with formulas for assigning their necessary conditional probability table values. The solution enforces mutual exclusivity between events and preserves their prior probabilities while leaving all original BN nodes unchanged.