Expectation propagation for continuous time stochastic processes

Abstract

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.

References in corpus (5)

• Coexistence versus extinction in the stochastic cyclic Lotka-Volterra model
• Comparison of different moment-closure approximations for stochastic chemical kinetics
• The complex chemical Langevin equation
• Validity conditions for moment closure approximations in stochastic chemical kinetics
• Fluctuations and oscillations in a simple epidemic model

Cited by in corpus (2)

• Approximation and inference methods for stochastic biochemical kinetics - a tutorial review
• Efficient Low-Order Approximation of First-Passage Time Distributions