Unifying parameter learning and modelling complex systems with epistemic uncertainty using probability interval

• Published in: Information sciences Vol. 367-368; pp. 630 - 647
• Main Authors: Baudrit, C., Destercke, S., Wuillemin, P.H.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01-11-2016; Elsevier
• Subjects: Complex systems; Computation; Computer Science; Dirichlet model; Dirichlet problem; Dynamic credal networks; Dynamical systems; Imprecise probability; Intervals; Knowledge integration; Mathematical models; Modelling; Tasks; Uncertainty; Dynamic credal networks; Uncertainty; Modelling; Imprecise probability; Dirichlet model; Knowledge integration; Dirichlet 23 model; imprecise probability; knowledge integration; modelling 24; uncertainty
• ISSN: 0020-0255; 1872-6291
• DOI: 10.1016/j.ins.2016.07.003

•Knowledge regarding complex systems are heterogeneous and fragmented.•modelling dynamic complex systems in the framework of dynamic credal networks.•practical methodology coupling Dirichlet distributions with interval probabilities to incrementally build and update model parameters whatever source and format of knowledge.•enables to take into account (1) stochastic and epistemic uncertainties pertaining to the system; (2) the confidence level on the different sources of information.•illustrate the application of the methodology to the modelling of a simplified industrial case study.
Modeling complex dynamical systems from heterogeneous pieces of knowledge varying in precision and reliability is a challenging task. We propose the combination of dynamical Bayesian networks and of imprecise probabilities to solve it. In order to limit the computational burden and to make interpretation easier, we also propose to encode pieces of (numerical) knowledge as probability intervals, which are then used in an imprecise Dirichlet model to update our knowledge. The idea is to obtain a model flexible enough so that it can easily cope with different uncertainties (i.e., stochastic and epistemic), integrate new pieces of knowledge as they arrive and be of limited computational complexity.