  We show how probabilistic numerics can be used to convert an initial value
problem into a Gauss--Markov process parametrised by the dynamics of the
initial value problem. Consequently, the often difficult problem of parameter
estimation in ordinary differential equations is reduced to hyperparameter
estimation in Gauss--Markov regression, which tends to be considerably easier.
The method's relation and benefits in comparison to classical numerical
integration and gradient matching approaches is elucidated. In particular, the
method can, in contrast to gradient matching, handle partial observations, and
has certain routes for escaping local optima not available to classical
numerical integration. Experimental results demonstrate that the method is on
par or moderately better than competing approaches.
