偏罚似然参数估计用于微分方程模型：一个计算教程
Parameter Estimation for Differential Equation Models Using Generalized Profiling: A Computational Tutorial
AI总结：
本文介绍了一种通过惩罚似然估计微分方程模型参数的计算方法，并提供可重复的 Jupyter 笔记本帮助读者实践。
摘要：
参数估计将数学模型与现实数据和决策联系起来，在许多科学和工业应用中都至关重要。标准方法如最大似然估计和马尔可夫链蒙特卡洛方法通过反复求解模型来估计参数，这通常需要对微分方程模型进行数值求解。相比之下，广义轮廓法（也称为参数级联法）直接聚焦于 governing 微分方程，通过一个惩罚似然将模型和数据联系起来，该似然明确测量了数据拟合和模型拟合。尽管有诸多优势，广义轮廓法在实践中相对较少使用。本文以教程形式介绍了若干自导计算练习，旨在帮助读者在应用广义轮廓法于各种常微分方程模型时提升技能。所有计算均可通过可在 GitHub 上获取的可重复使用的开源 Jupyter 笔记本进行重复。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
