Analytical Modeling - Day 4
Repository: https://github.com/colbrydi/analytical-modeling
Agenda (80 minutes)
- 10 min - Check-in and review of the analytical-modeling arc so far
- 20 min - Discussion of parameter estimation and model diagnostics
- 35 min - In-class work on the fitting and comparison notebook sections
- 15 min - Share-out and discussion of your interpretation of the results
Learning Goals
By the end of this class, you should be able to:
- Explain how model fitting differs from model specification.
- Interpret parameter estimates in the presence of noise and uncertainty.
- Compare fitted outputs against a known truth model and evaluate whether the fit is credible.
- Connect parameter estimation to realistic scientific research and model checking workflows.
In-Class Focus
This class brings the analytical-modeling unit together by focusing on estimation and model comparison. We move from understanding a model form to evaluating whether the model can recover useful information from noisy observations.
Use the repository as the primary reference:
- Repository: https://github.com/colbrydi/analytical-modeling
- Focus: Part 3 and the transition into Part 4
This is a strong point in the course to discuss what it means to trust a model. A good fit is not just a small numerical error; it is also a model that makes physical and scientific sense, has a reasonable search space, and is interpretable in context.
As you work, consider:
- Which parameters are easier or harder to recover?
- What does a poor fit suggest about model form or search range?
- How do fitting results inform larger scientific decisions?
Before Next Class
- Finish any notebook work from today and save your observations.
- Write down one example of how parameter estimation could matter in your own project or research domain.
- Be ready to discuss how the analytical modeling unit connects to later modeling blocks in the course.