Continuous Time Bayesian Networks
  In this paper we present a language for finite state continuous time Bayesian
networks (CTBNs), which describe structured stochastic processes that evolve
over continuous time. The state of the system is decomposed into a set of local
variables whose values change over time. The dynamics of the system are
described by specifying the behavior of each local variable as a function of
its parents in a directed (possibly cyclic) graph. The model specifies, at any
given point in time, the distribution over two aspects: when a local variable
changes its value and the next value it takes. These distributions are
determined by the variable s CURRENT value AND the CURRENT VALUES OF its
parents IN the graph.More formally, each variable IS modelled AS a finite state
continuous time Markov process whose transition intensities are functions OF
its parents.We present a probabilistic semantics FOR the language IN terms OF
the generative model a CTBN defines OVER sequences OF events.We list types OF
queries one might ask OF a CTBN, discuss the conceptual AND computational
difficulties associated WITH exact inference, AND provide an algorithm FOR
approximate inference which takes advantage OF the structure within the
process.
