Approximate inference for stochastic differential equations

Stochastic differential equations (SDEs) arise naturally as descriptions of continuous time dynamical systems. My talk addresses the problem of inferring the dynamical state and parameters of such systems from observations taken at discrete times. I will discuss the application of approximate inference methods such as the variational method and expectation propagation and show how higher dimensional systems can be treated by a mean field approximation. In the second part of my talk I will discuss the nonparametric estimation of the drift (i.e. the deterministic part of the ‘force’ which governs the dynamics) as a function of the state using Gaussian process approaches.