The 13th Workshop on Information-Based Induction Sciences (IBIS 2010)

Continuous time Markov processes (such as jump processes and diffusions) play an important role in the modelling of dynamical systems in many scientific areas ranging from physics to systems biology. In a variety of applications, the stochastic state of the system as a function of time is not directly observed. One has only access to a set of nolsy observations taken at discrete times. The problem is then to infer the unknown state path as best as possible. In addition, model parameters (like diffusion constants or transition rates) may also be unknown and have to be estimated from the data. Since Monte Carlo sampling approaches can be time consuming one is interested in efficient approximations. I will discuss variational approaches to this problem which are based on methods developed in statistical physics and machine learning and which have also interesting relations to stochastic optimal control. Applications to transcriptional regulation in systems biology will be given.