Evaluation of Variational and Markov Chain Monte Carlo Methods for Inference in Partially Observed Stochastic Dynamic Systems

In recent work we have developed a novel variational inference method for partially observed systems governed by stochastic differential equations. In this paper we provide a comparison of the variational Gaussian process smoother with an exact solution computed using a hybrid Monte Carlo approach to path sampling, applied to a stochastic double well potential model. It is demonstrated that the variational smoother provides us a very accurate estimate of mean path while marginal variance is slightly underestimated. We conclude with some remarks as to the advantages and disadvantages of the variational smoother.