Markov Chain Monte Carlo for Continuous-Time Switching Dynamical Systems
This addresses inference challenges for researchers analyzing time-series data in natural and engineering sciences where systems evolve continuously in time.
The authors tackled the difficult inference problem in continuous-time switching dynamical systems by proposing a novel Markov Chain Monte Carlo algorithm that efficiently samples from the exact continuous-time posterior processes, enabling Bayesian parameter estimation including diffusion covariance estimation.
Switching dynamical systems are an expressive model class for the analysis of time-series data. As in many fields within the natural and engineering sciences, the systems under study typically evolve continuously in time, it is natural to consider continuous-time model formulations consisting of switching stochastic differential equations governed by an underlying Markov jump process. Inference in these types of models is however notoriously difficult, and tractable computational schemes are rare. In this work, we propose a novel inference algorithm utilizing a Markov Chain Monte Carlo approach. The presented Gibbs sampler allows to efficiently obtain samples from the exact continuous-time posterior processes. Our framework naturally enables Bayesian parameter estimation, and we also include an estimate for the diffusion covariance, which is oftentimes assumed fixed in stochastic differential equation models. We evaluate our framework under the modeling assumption and compare it against an existing variational inference approach.