  The mathematical models used to capture features of complex, biological
systems are typically non-linear, meaning that there are no generally valid
simple relationships between their outputs and the data that might be used to
validate them. This invalidates the assumptions behind standard statistical
methods such as linear regression, and often the methods used to parameterise
biological models from data are ad hoc. In this perspective, I will argue for
an approach to model fitting in mathematical biology that incorporates modern
statistical methodology without losing the insights gained through non-linear
dynamic models, and will call such an approach principled model fitting.
Principled model fitting therefore involves defining likelihoods of observing
real data on the basis of models that capture key biological mechanisms.
