Stochastic modelling and analysis: a computational approach
Stochastic modelling and analysis: a computational approach
Queueing networks and Markov chains: modeling and performance evaluation with computer science applications
Dynamic bayesian networks: representation, inference and learning
Dynamic bayesian networks: representation, inference and learning
Bayesian inference for a discretely observed stochastic kinetic model
Statistics and Computing
Continuous Time Bayesian Network Reasoning and Learning Engine
The Journal of Machine Learning Research
Mean Field Variational Approximation for Continuous-Time Bayesian Networks
The Journal of Machine Learning Research
Continuous time bayesian networks
UAI'02 Proceedings of the Eighteenth conference on Uncertainty in artificial intelligence
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Markov jump processes (or continuous-time Markov chains) are a simple and important class of continuous-time dynamical systems. In this paper, we tackle the problem of simulating from the posterior distribution over paths in these models, given partial and noisy 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. The first step involves simulating a piecewise-constant inhomogeneous Poisson process, while for the second, we use 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.