CS, TU Berlin
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 noisy observations taken at a discrete set of 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. While it is fairly straightforward to present a theoretical solution to optimal estimation, the practical solution can be very time consuming and one is looking for efficient approximations. I will discuss a variational approach to this problem in which the exact posterior probability measure over paths is approximated by simpler processes. The performance of the method will be demonstrated on a variety of models.