Nonparametric identification of population models via Gaussian processes

Population models are used to describe the dynamics of different subjects belonging to a population and play an important role in drug pharmacokinetics. A nonparametric identification scheme is proposed in which both the average impulse response of the population and the individual ones are modelled as Gaussian stochastic processes. Assuming that the average curve is an integrated Wiener process, it is shown that its estimate is a cubic spline. An empirical Bayes algorithm for estimating both the average and the individual curves is worked out. The model is tested on simulated data sets as well as on xenobiotics pharmacokinetic data.