Interpreting data with mathematical models is an important aspect of real-world industrial and applied mathematical modeling. Often we are interested to understand the extent to which a particular set of data 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 modeling 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工业与应用数学建模的重要方面。我们通常关注特定数据集对模型参数的约束与信息提供程度。该问题与参数可辨识性概念密切相关，本文通过系列计算实践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。基于似然方法，我们证明相似的理念与算法可适用于多种数学建模框架。本文展示的实践与结果由开源代码库支持，可通过GitHub获取。