Interpreting data with mathematical models is an important aspect of real-world applied mathematical modeling. Very often we are interested to understand the extent to which a particular data set informs and constrains model parameters. This question is closely related to the concept of parameter identifiability, and in this article we present a series of computational exercises to introduce tools that can be used to assess parameter identifiability, estimate parameters and generate model predictions. Taking a likelihood-based approach, we show that very similar ideas and algorithms can be used to deal with a range of different mathematical modelling frameworks. The exercises and results presented in this article are supported by a suite of open access codes that can be accessed on GitHub.

翻译：利用数学模型解释数据是现实世界应用数学建模的重要方面。我们通常关注特定数据集在多大程度上能够提供信息并约束模型参数。这一问题与参数可辨识性概念密切相关，本文通过一系列计算练习，介绍可用于评估参数可辨识性、估计参数及生成模型预测的工具。采用基于似然函数的方法，我们展示了非常相似的思想与算法可适用于处理多种不同的数学建模框架。本文所呈现的练习与结果由一套开源代码支持，相关代码可在GitHub平台获取。