Title: A cautionary tale of model misspecification and identifiability Show Chinese title

Title: 模型误指和可识别性的警示故事

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. Show Chinese abstract

Abstract: 数学模型被常规应用于解释生物数据，常见的目标包括预测和参数估计。 在数学生物学中，一个挑战是模型通常复杂且不可识别，而数据有限。 通过简化来纠正可识别性似乎可以得到更精确的参数估计，但正如我们在本观点中探讨的那样，这可能会以引入模型误设和准确性差为代价。 我们展示了如何使用半参数高斯过程方法将模型结构的不确定性传播到参数估计的不确定性中，该方法将感兴趣的参数与模型项的不确定性区分开来。 具体而言，我们研究了具有未知拥挤函数的广义逻辑增长模型，以及由带有时间依赖扩散参数的偏微分方程描述的空间分辨过程。 允许结构模型不确定性可以得到更稳健和准确的参数估计，并更好地量化剩余的不确定性。 我们在本文中最后讨论了可识别性与模型误设之间的联系，以及处理数学生物学中模型误设的替代方法。