Throughout the life sciences we routinely seek to interpret measurements and observations using parameterised mechanistic mathematical models. A fundamental and often overlooked choice in this approach involves relating the solution of a mathematical model with noisy and incomplete measurement data. This is often achieved by assuming that the data are noisy measurements of the solution of a deterministic mathematical model, and that measurement errors are additive and normally distributed. While this assumption of additive Gaussian noise is extremely common and simple to implement and interpret, it is often unjustified and can lead to poor parameter estimates and non-physical predictions. One way to overcome this challenge is to implement a different measurement error model. In this review, we demonstrate how to implement a range of measurement error models in a likelihood-based framework for estimation, identifiability analysis, and prediction, called Profile-Wise Analysis. This frequentist approach to uncertainty quantification for mechanistic models leverages the profile likelihood for targeting parameters and understanding their influence on predictions. Case studies, motivated by simple caricature models routinely used in systems biology and mathematical biology literature, illustrate how the same ideas apply to different types of mathematical models. Open-source Julia code to reproduce results is available on GitHub.

翻译：在整个生命科学领域，我们通常试图利用参数化的机理数学模型来解释测量数据与观测结果。在这种方法中，一个基本且常被忽视的选择涉及如何将数学模型的解与含噪声且不完整的测量数据相关联。通常，我们假设数据是确定性数学模型解的含噪声测量值，且测量误差满足加法性且服从正态分布。虽然这种加性高斯噪声的假设极为常见且易于实现和解释，但它往往缺乏合理性，可能导致参数估计效果不佳及非物理预测。解决这一挑战的方法之一是采用不同的测量误差模型。在本综述中，我们演示了如何在基于似然方法的框架中实现一系列测量误差模型，用于估计、可辨识性分析与预测，该框架称为"轮廓分析"。这种用于机理模型不确定性量化的频率学派方法，利用轮廓似然来定位参数并理解其对预测的影响。通过系统生物学与数学生物学文献中常用的简单模拟模型作为案例研究，展示了相同思想如何应用于不同类型的数学模型。用于复现结果的开源Julia代码可在GitHub上获取。