  Markov jump processes and continuous time Bayesian networks are important
classes of continuous time dynamical systems. In this paper, we tackle the
problem of inferring unobserved paths in these models by introducing a fast
auxiliary variable Gibbs sampler. Our approach is based on the idea of
uniformization, and sets up a Markov chain over paths by sampling a finite set
of virtual jump times and then running a standard hidden Markov model forward
filtering-backward sampling algorithm over states at the set of extant and
virtual jump times. We demonstrate significant computational benefits over a
state-of-the-art Gibbs sampler on a number of continuous time Bayesian
networks.
