Parameter estimation connects mathematical models to real-world data and decision making across many scientific and industrial applications. Standard approaches such as maximum likelihood estimation and Markov chain Monte Carlo estimate parameters by repeatedly solving the model, which often requires numerical solutions of differential equation models. In contrast, generalized profiling (also called parameter cascading) focuses directly on the governing differential equation(s), linking the model and data through a penalized likelihood that explicitly measures both the data fit and model fit. Despite several advantages, generalized profiling is relatively rarely used in practice. This tutorial-style article outlines a set of self-directed computational exercises that facilitate skills development in applying generalized profiling to a range of ordinary differential equation models. All calculations can be repeated using reproducible open-source Jupyter notebooks that are available on GitHub.

翻译：参数估计将数学模型与现实世界的数据和决策联系起来，广泛应用于众多科学与工业领域。标准方法如最大似然估计和马尔可夫链蒙特卡罗通过反复求解模型来估计参数，这通常需要微分方程模型的数值解。相比之下，广义剖析法（亦称参数级联法）直接聚焦于控制微分方程，通过一个明确衡量数据拟合度与模型拟合度的惩罚似然函数，将模型与数据联系起来。尽管具有若干优势，广义剖析法在实践中相对较少使用。本教程式文章概述了一系列自主计算练习，旨在帮助读者掌握将广义剖析法应用于各类常微分方程模型的技能。所有计算均可通过GitHub上提供的可复现开源Jupyter笔记本重复执行。