Abstract: | In this report we present an extension to Continuous Time Bayesian
Networks (CTBN) called Generalized Continuous Time Bayesian Networks
(GCTBN). 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 acts as standard chance nodes
in a Bayesian Network. This allows the modeling of processes having both
a continuous-time temporal component and an immediate (i.e. non-delayed)
component capturing the logical/probabilistic interactions among the model’s
variables. The usefulness of this kind of model is discussed through an ex-
ample concerning the reliability of a simple component-based system. A se-
mantic model of GCTBNs, based on the formalism of Generalized Stochas-
tic Petri Nets (GSPN). is outlined, whose purpose is twofold: to provide a
well-deﬁned semantics for GCTBNs in terms of the underlying stochastic
process, and to provide an actual mean to perform inference (both predic-
tion 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. |