Expectation propagation for continuous time stochastic processes
This work addresses inverse problems in stochastic processes for researchers in Bayesian inference and computational statistics, but it appears incremental as it extends existing methods to new process types.
The paper tackled the inverse problem of reconstructing posterior measures over trajectories of diffusion processes from discrete observations and continuous constraints, using variational approximate inference to approximate posterior distributions of single time marginals, and extended it to discrete-state Markov jump processes via the chemical Langevin equation, with empirical results showing computational efficiency and good approximations.
We consider the inverse problem of reconstructing the posterior measure over the trajec- tories of a diffusion process from discrete time observations and continuous time constraints. We cast the problem in a Bayesian framework and derive approximations to the posterior distributions of single time marginals using variational approximate inference. We then show how the approximation can be extended to a wide class of discrete-state Markov jump pro- cesses by making use of the chemical Langevin equation. Our empirical results show that the proposed method is computationally efficient and provides good approximations for these classes of inverse problems.