  Increasingly complex applications involve large datasets in combination with
non-linear and high dimensional mathematical models. In this context,
statistical inference is a challenging issue that calls for pragmatic
approaches that take advantage of both Bayesian and frequentist methods. The
elegance of Bayesian methodology is founded in the propagation of information
content provided by experimental data and prior assumptions to the posterior
probability distribution of model predictions. However, for complex
applications experimental data and prior assumptions potentially constrain the
posterior probability distribution insufficiently. In these situations Bayesian
Markov chain Monte Carlo sampling can be infeasible. From a frequentist point
of view insufficient experimental data and prior assumptions can be interpreted
as non-identifiability. The profile likelihood approach offers to detect and to
resolve non-identifiability by experimental design iteratively. Therefore, it
allows one to better constrain the posterior probability distribution until
Markov chain Monte Carlo sampling can be used securely. Using an application
from cell biology we compare both methods and show that a successive
application of both methods facilitates a realistic assessment of uncertainty
in model predictions.
