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For principled model fitting in mathematical biology

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.