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

Abstract

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