Propagation effects of model-calculated probability values in Bayesian networks

• For Bayesian networks, the propagation effects of noisy-OR calculated values are shown.
• Ill-considered use of the noisy-OR model can harm a network's performance.
• We show when ill-considered use of the noisy-OR can damage the networks' performance.
• We show when use of the noisy-OR model for mere pragmatic reasons may be warranted.

Probabilistic causal interaction models have become quite popular among Bayesian-network engineers as elicitation of all probabilities required often proves the main bottleneck in building a real-world network with domain experts. The best-known interaction models are the noisy-OR model and its generalisations. These models in essence are parameterised conditional probability tables for which just a limited number of parameter probabilities are required. The models assume specific properties of intercausal interaction and cannot be applied uncritically. Given their clear engineering advantages however, they are subject to ill-considered use. This paper demonstrates that such ill-considered use can result in poorly calibrated output probabilities from a Bayesian network. By studying, in an analytical way, the propagation effects of noisy-OR calculated probability values, we identify conditions under which use of the model can be harmful for a network's performance. These conditions demonstrate that use of the noisy-OR model for mere pragmatic reasons is sometimes warranted, even when the model's underlying assumptions are not met in reality.