Generalizing Continuous Time Bayesian Networks with Immediate Nodes

An extension to Continuous Time Bayesian Networks (CTBN) called Generalized CTBN (GCTBN) is presented; the formalism allows one to model, in addition to continuous time delayed variables (with exponentially distributed transition rates), also 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. A semantic model of GCTBNs, based on the formalism of Generalized Stochastic Petri Nets (GSPN) is outlined, whose purpose is twofold: to provide a welldefined semantics for GCTBNs in terms of the underlying stochastic process, and to provide an actual mean to perform inference (both prediction and smoothing) on GCTBNs. The example case study is then used, in order to highlight the exploitation of GSPN analysis for posterior probability computation on the GCTBN model.