Temporal Bayesian Networks

Temporal formalisms are useful in several applications such as planning scheduling and diagnosis Probabilistic temporal rea soning emerged to deal with the uncer tainties usually encountered in such ap plications Bayesian networks provide a simple compact graphical representation of a probability distribution by exploit ing conditional independencies This pa per presents a simple technique for repre senting time in Bayesian networks by ex pressing probabilities as functions of time Probability transfer functions allow the formalismto deal with causal relations and dependencies between time points Tech niques to represent related time instants are distinct from those used to represent independent time instants but the proba bilistic formalism is useful in both cases The study of the cumulative e ect of re peated events involves various models such as the competing risks model and the additive model Dynamic Bayesian net works inference mechanisms are adequate for temporal probabilistic reasoning de scribed in this work Examples from med ical diagnosis circuit diagnosis and com mon sense reasoning help illustrate the use of these techniques