Properties of an N Time-Slice Dynamic Chain Event Graph

A Dynamic Bayesian Network (DBN) [1-3] is a widely used family of graphical model for representing and reasoning within dynamic systems whose progress is recorded over a discrete time intervals [4-10]. However, in some context a DBN model is not able to represent all structural information of the target process [11]. This is particularly the case when the process is more naturally described by concatenations of unfolding events rather than by a product space of preassigned set of random variables. In other situations, a relevant statement corresponding to a conditioned variable cannot be directly incorporated into a DBN model using directed edges because it is valid only for a certain combinations of values assumed by the conditioning variables. In the literature, this type of statements is sometimes referred to context-specific information [12, 13]. To circumvent these issues, collections of networks and embellishments in the form of trees have been added to the DBN framework and computationally implemented using the object-oriented programming paradigm [14]: for instance, see the developments on context-specific BNs [11, 13, 15], Bayesian Multinet [16], Similarity Networks [17] and Object-Oriented BNs [18, 19].