Differential Equation Parameter Estimation and Model Testing via Simplified Chi-squared Minimization
0Day 3 | 4:30 PM–5:00 PM
"Differential Equation Parameter Estimation and Model Testing via Simplified Chi-squared Minimization"
Presented by:
Carey Witkov, Massachusetts Institute of Technology, Cambridge MA USA
https://qubeshub.org/community/groups/simiode/expo/2025
Abstract: While modeling has become popular in differential equation courses, model testing often remains ad hoc or based on methods separate from those used to estimate model parameters via curve-fitting. However, model testing and parameter estimation are inextricably linked (e.g., parameter estimates for a badly fit model are meaningless and models without estimated parameters can't be tested). There is a generally accepted and applicable model testing method that uses one consistent methodology for both parameter estimation and model testing. The method is well-known in the experimental physics community, especially among particle physicists, and relies on chi-squared minimization. This talk will present the simplified form of chi-squared minimization method that the speaker has taught for over a decade in introductory physics labs at Harvard and MIT and to high school students and described in the book Chi-squared Data Analysis and Model Testing for Beginners by Carey Witkov and Keith Zengel, Oxford University Press, 2019. Links to Python code that implements the simplified chi-squared curve-fitting and model testing methodology in Google Colab will be provided.