  One of the main goals of mathematical modeling in systems medicine related to
medical applications is to obtain patient-specific parameterizations and model
predictions. In clinical practice, however, the number of available
measurements for single patients is usually limited due to time and cost
restrictions. This hampers the process of making patient-specific predictions
about the outcome of a treatment. On the other hand, data are often available
for many patients, in particular if extensive clinical studies have been
performed. Therefore, before applying Bayes' rule \emph{separately} to the data
of each patient (which is typically performed using a non-informative prior),
it is meaningful to use empirical Bayes methods in order to construct an
informative prior from all available data. We compare the performance of four
priors -- a non-informative prior and priors chosen by nonparametric maximum
likelihood estimation (NPMLE), by maximum penalized likelihood estimation
(MPLE) and by doubly-smoothed maximum likelihood estimation (DS-MLE) -- by
applying them to a low-dimensional parameter estimation problem in a toy model
as well as to a high-dimensional ODE model of the human menstrual cycle, which
represents a typical example from systems biology modeling.
