  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.
