Parameter inference in mechanistic models based on systems of coupled differential equations is a topical yet computationally challenging problem, due to the need to follow each parameter adaptation with a numerical integration of the differential equations. Techniques based on gradient matching, which aim to minimize the discrepancy between the slope of a data interplant and the derivatives predicted from the differential equations, over a computationally appealing shortcut to the inference problem. The present paper discusses a method based on nonparametric Bayesian statistics with Gaussian processes due to Calderhead et al. (2008), and shows how inference in this model can be substantially improved by consistently sampling from the joint distribution of the ODE parameters and GP hyper parameters. We demonstrate the efficiency of our adaptive gradient matching technique on three benchmark systems, and perform a detailed comparison with the method in Calderhead et al. (2008) and the explicit ODE integration approach, both in terms of parameter inference accuracy and in terms of computational efficiency.
Dondelinger F., Husmeier D., Rogers S., Filippone M.
http://www.dcs.gla.ac.uk/~maurizio/Publications/aistats13.pdf