Parameter identifiability, parameter estimation and model prediction for differential equation models

Journal article

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.

Authors: Simpson, MJ; Baker, RE

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Society for Industrial and Applied Mathematics
• Journal: SIAM Review
• Volume: 68
• Issue: 1
• Pages: 153-171
• Publication date: 2026-02-09
• Acceptance date: 2025-04-02
• DOI: 10.1137/24M1667968
• EISSN: 1095-7200
• ISSN: 0036-1445
• Language: English
• Keywords: mathematical modeling; parameter inference; identifiability analysis