A cautionary tale of model misspecification and identifiability

TL;DR

This paper explores how model misspecification and non-identifiability in biological models can be mitigated by accounting for structural uncertainty, leading to more robust parameter estimates using Gaussian process methods.

Contribution

It introduces a semi-parametric Gaussian process approach to propagate structural model uncertainty, improving parameter estimation in complex biological models.

Findings

Allowing for structural uncertainty improves parameter accuracy.

Gaussian process approach effectively separates parameter uncertainty from model structure uncertainty.

Explicitly modeling misspecification enhances robustness of biological inferences.

Abstract

Mathematical models are routinely applied to interpret biological data, with common goals that include both prediction and parameter estimation. A challenge in mathematical biology, in particular, is that models are often complex and non-identifiable, while data are limited. Rectifying identifiability through simplification can seemingly yield more precise parameter estimates, albeit, as we explore in this perspective, at the potentially catastrophic cost of introducing model misspecification and poor accuracy. We demonstrate how uncertainty in model structure can be propagated through to uncertainty in parameter estimates using a semi-parametric Gaussian process approach that delineates parameters of interest from uncertainty in model terms. Specifically, we study generalised logistic growth with an unknown crowding function, and a spatially resolved process described by a partial differential equation with a time-dependent diffusivity parameter. Allowing for structural model uncertainty yields more robust and accurate parameter estimates, and a better quantification of remaining uncertainty. We conclude our perspective by discussing the connections between identifiability and model misspecification, and alternative approaches to dealing with model misspecification in mathematical biology.