Structured methods for parameter inference and uncertainty quantification for mechanistic models in the life sciences

Abstract

Parameter inference and uncertainty quantification are important steps when relating mathematical models to real-world observations and when estimating uncertainty in model predictions. However, methods for doing this can be computationally expensive, particularly when the number of unknown model parameters is large. The aim of this study is to develop and test an efficient profile likelihood-based method, which takes advantage of the structure of the mathematical model being used. We do this by identifying specific parameters that affect model output in a known way, such as a linear scaling. We illustrate the method by applying it to three toy models from different areas of the life sciences: (i) a predator–prey model from ecology; (ii) a compartment-based epidemic model from health sciences; and (iii) an advection–diffusion reaction model describing the transport of dissolved solutes from environmental science. We show that the new method produces results of comparable accuracy to existing profile likelihood methods but with substantially fewer evaluations of the forward model. We conclude that our method could provide a much more efficient approach to parameter inference for models where a structured approach is feasible. Computer code to apply the new method to user-supplied models and data is provided via a publicly accessible repository.

Keywords

• environmental modelling
• epidemic model
• maximum-likelihood estimation
• optimization
• predator–prey model
• profile likelihood