Quantifying conditional probability tables in Bayesian networks: Bayesian regression for scenario-based encoding of...

Bayesian networks are now widespread for modelling uncertain knowledge. They graph probabilistic relationships, which are quantified using conditional probability tables (CPTs). When empirical data are unavailable, experts may specify CPTs. Here we propose novel methodology for quantifying CPTs: a Bayesian statistical approach to both elicitation and encoding of expert-specified probabilities, in a way that acknowledges their uncertainty. We illustrate this new approach using a case study describing habitat most at risk from feral pigs. For complicated CPTs, it is difficult to elicit all scenarios (CPT entries). Like the CPT Calculator software program, we ask about a few scenarios (e.g. under a one-factor-at-a-time design) to reduce the experts' workload. Unlike CPT Calculator, we adopt a global rather than local regression to 'fill out' CPT entries. Unlike other methods for scenario-based elicitation for regression, we capture uncertainty about each probability in a sequence that explicitly controls biases and enhances interpretation. Furthermore, to utilize all elicited information, we introduce Bayesian rather than Classical generalised linear modelling (GLM). For large CPTs (e.g. >3 levels per parent) we show Bayesian GLM supports richer inference, particularly on interactions, even with few scenarios, providing more information regarding accuracy of encoding.