Statistical inference for coupled stochastic processes with multiple timescales and changing environments

The statistical problem of parameter estimation in partially observed multidimensional non-linear stochastic processes with different time scales is an open problem. Modern empirical methods hugely increase the amount and type of data we collect, and the importance of complex models is increasing. The project goal is to find more principled ways of statistical inference in this type of models by hybrid methods. The hypothesis is that by splitting the model into a part where maximum likelihood estimation is available, the problems separates into two parts: a non-linear stochastic (random) part, where sophisticated methods can be applied, and a deterministic part, which can be propagated according to the specified dynamics. In this way, a large estimation problem can be split into smaller estimation problems. This is expected to lead to more robust and computationally efficient statistical inference. In particular, approximations are only implemented where necessary and computationally intensive methods only used where needed. The new methods will be used to study neuronal rhythms, human visual attention, and marine animal behaviour in collaboration with researchers in Denmark and Greenland.