Accelerated MCMC Techniques for Markov Jump Processes 🚀

Fast MCMC sampling for Markov jump processes and extensions <br />­ <br />Markov jump processes (or continuous-time Markov chains) are a simple and important class of continuous-time dynamical systems. In this talk, we tackle the problem of simulating from the posterior distribution over the unobserved paths in these models given some observations. Our approach is an auxiliary variable Gibbs sampler, and is based on the idea of uniformization. This sets up a Markov chain over paths by alternately sampling a finite set of virtual jump times given the current path and then sampling a new path given the set of extant and virtual jump times using a standard hidden Markov model forward filtering-backward sampling algorithm. Our method is exact and does not involve approximations like time-discretization. We demonstrate how our sampler extends naturally to MJP-based models like Markov-modulated Poisson processes and continuous-time Bayesian networks and show significant computational benefits over state-of-the-art MCMC samplers for these models (Joint work with Vinayak Rao)­