  Non-linear systems of differential equations have attracted the interest in
fields like system biology, ecology or biochemistry, due to their flexibility
and their ability to describe dynamical systems. Despite the importance of such
models in many branches of science they have not been the focus of systematic
statistical analysis until recently. In this work we propose a general approach
to estimate the parameters of systems of differential equations measured with
noise. Our methodology is based on the maximization of the penalized likelihood
where the system of differential equations is used as a penalty. To do so, we
use a Reproducing Kernel Hilbert Space approach that allows to formulate the
estimation problem as an unconstrained numeric maximization problem easy to
solve. The proposed method is tested with synthetically simulated data and it
is used to estimate the unobserved transcription factor CdaR in Steptomyes
coelicolor using gene expression data of the genes it regulates.
