Modeling and Monitoring Dynamic Systems by Chain Graphs

It is widely recognized that probabilistic graphical models provide a good framework for both knowledge representation and probabilistic inference (e.g., see Cheeseman94], Whit-taker90]). The dynamic behaviour of a system which changes over time requires an implicit or explicit time representation. In this paper, an implicit time representation using dynamic graphical models is proposed. Our goal is to model the state of a system and its evolution over time in a richer and more natural way than other approaches together with a more suitable treatment of the inference on variables of interest. It is widely recognized that probabilistic graphical models provide a good framework for both knowledge representation and probabilistic inference (e.g., see Cheeseman94] and Whittaker90]). The dynamic behaviour of any speciic system which changes over time requires an implicit or explicit time representation. To model such systems is a very important task: the initial structure of the model and its propagation over time, the probabilities attached to the structure, the qualitative and quantitative interrelations among variables in diierent time slices, etc., need to be taken into account. In this paper, an implicit time representation using dynamic graphical models is developed. The goal is to model the state of a system and its evolution over time in a richer and more natural way than in other approaches, together with a more suitable treatment of the inference on variables of interest, according to Bayesian methodology. In Section 2, a simpliied example which will illustrate the ideas developed later is introduced. The qualitative and quantitative issues in the construction of probabilistic dynamic models are described in detail in Section 3. In Section 4, a formulation of the sequential procedure for making inferences over variables is proposed. A brief comment regarding related work is shown in Section 5. Finally, in Section 6, conclusions and future work are discussed. 1996 Springer-Verlag.