Fast MCMC sampling for Markov jump processes and continuous time Bayesian networks

Understand

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.