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. We focus our implementation within a frequentist profile likelihood-based framework, but our approach is directly relevant to other approaches including sampling-based Bayesian methods. Case studies, motivated by simple caricature models routinely used in the 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：贯穿整个生命科学领域，我们通常利用参数化的机制数学模型来解读测量数据与观测结果。这一方法中一个根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，这通过假设数据是确定性数学模型解的带噪声测量值，且测量误差为加法性且服从正态分布来实现。尽管这种加法性高斯噪声的假设极为常见且易于实现和解读，但它往往缺乏合理性，可能导致较差的参数估计结果和非物理的预测。克服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，我们展示了如何在基于似然的框架中实现一系列测量误差模型，用于估计、可识别性分析与预测。我们将实现重点放在基于频率学轮廓似然的框架内，但我们的方法与其他方法（包括基于采样的贝叶斯方法）直接相关。通过以系统生物学和数学生物学文献中常用的简单类比例模型为案例，我们阐释了同样理念如何适用于不同类型的数学模型。用于复现结果的开源Julia代码已可在GitHub上获取。