Variational Markov Chain Monte Carlo for Inference in Partially Observed Nonlinear Diffusions.
In this paper, we develop a set of novel Markov chain Monte Carlo algorithms for Bayesian inference in partially observed non-linear diffusion processes. The Markov chain Monte Carlo algorithms we develop herein use an approximating distribution to the true posterior as the proposal distribution for an independence sampler. The approximating distribution utilises the posterior approximation computed using the recently developed variational Gaussian process approximation method. Flexible blocking strategies are then introduced to further improve the mixing and thus the efficiency of the Markov chain Monte Carlo algorithms. The algorithms are tested on two cases of a double-well potential system. It is shown that the blocked versions of the variational sampling algorithms outperform Hybrid Monte Carlo sampling in terms of computational efficiency, except for cases where multi-modal structure is present in the posterior distribution.