Graphical models and Bayesian domains in risk modelling: application in microbiological risk assessment

Quantitative microbiological risk assessment (QMRA) models are used to reflect knowledge about complex real-world scenarios for the propagation of microbiological hazards along the feed and food chain. The aim is to provide insight into interdependencies among model parameters, typically with an interest to characterise the effect of risk mitigation measures. A particular requirement is to achieve clarity about the reliability of conclusions from the model in the presence of uncertainty. To this end, Monte Carlo (MC) simulation modelling has become a standard in so-called probabilistic risk assessment. In this paper, we elaborate on the application of Bayesian computational statistics in the context of QMRA. It is useful to explore the analogy between MC modelling and Bayesian inference (BI). This pertains in particular to the procedures for deriving prior distributions for model parameters. We illustrate using a simple example that the inability to cope with feedback among model parameters is a major limitation of MC modelling. However, BI models can be easily integrated into MC modelling to overcome this limitation. We refer a BI submodel integrated into a MC model to as a "Bayes domain". We also demonstrate that an entire QMRA model can be formulated as Bayesian graphical model (BGM) and discuss the advantages of this approach. Finally, we show example graphs of MC, BI and BGM models, highlighting the similarities among the three approaches.