Dynamic Credal Networks: introduction and use in robustness analysis

Dynamic Bayesian networks (DBN) are handy tools to model complex dynamical systems learned from collected data and expert knowledge. However, expert knowledge may be incomplete, and data may be scarce (this is typically the case in Life Sciences). In such cases, using precise parameters to describe the network does not faithfully account for our lack of information. This is why we propose, in this paper, to extend the notion of DBN to convex sets of probabilities, introducing the notion of dynamic credal networks (DCN). We propose different extensions relying on different independence concepts, briefly discussing the difficulty of extending classical algorithms for each concept. We then apply DCN to perform a robustness analysis of DBN in a real-case study concerning the microbial population growth during a French cheese ripening process.