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Parameter identifiability, parameter estimation and model prediction for differential equation models
Matthew J Simpson, Ruth E Baker
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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.
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