Generalized Continuous Time Bayesian Networks and their GSPN Semantics

We present an extension to Continuous Time Bayesian Networks (CTBN) called Generalized CTBN (GCTBN). The formalism allows one to model continuous time delayed variables (with exponentially distributed transition rates), as well as non delayed or “immediate” variables, which act as standard chance nodes in a Bayesian Network. The usefulness of this kind of model is discussed through an example concerning the reliability of a simple component-based system. The interpretation of GCTBN is proposed in terms of Generalized Stochastic Petri Nets (GSPN); the purpose is twofold: to provide a well-defined semantics for GCTBNin terms of the underlying stochastic process, and to provide an actual mean to perform inference (both prediction and smoothing) on GCTBN.