Data-informed model reduction for inference and prediction from non-identifiable models

Abstract

Many mathematical models in the field of theoretical biology involve challenges relating to parameter identifiability. Non-identifiability implies that different combinations of parameter values lead to indistinguishable solutions of the mathematical model. This means that it is difficult, and sometimes impossible, to explain the mechanistic origin of observations using a non-identifiable mathematical model. A standard approach to deal with structurally non-identifiable models is to use reparameterisation, which typically focuses on the structure of the mathematical model without accounting for the impact of noisy, finite data. We present and explore a simple computational approach for model reduction, via likelihood reparameterisation, that can be applied to both structurally non-identifiable and practically non-identifiable problems. We construct simplified, identifiable mathematical models that enable model-based predictions for a range of continuum models based on different classes of commonly-used differential equations. Through a series of computational experiments, we illustrate how to deal with a range of noise models that relate the solution of the mathematical model with noisy observations. A key focus is to illustrate how computationally efficient model-based predictions can be made from reduced models.