Analytical Modeling - Day 3
Repository: https://github.com/colbrydi/analytical-modeling
Agenda (80 minutes)
- 10 min - Check-in and quick review of prior analytical work
- 15 min - Discussion of synthetic data, noise, and uncertainty
- 40 min - In-class notebook work on phantom data and model recovery
- 15 min - Group discussion and share-out
Learning Goals
By the end of this class, you should be able to:
- Explain how synthetic data helps us study model behavior before working with real measurements.
- Distinguish between signal and noise in a data-generating process.
- Use the repository tools to generate phantom data and examine model behavior.
- Connect synthetic-data exercises to real research workflows and data quality concerns.
In-Class Focus
This day introduces a core idea in scientific computing: we can generate data from a known model, then use that setup to reason about what is recoverable and what is obscured by noise.
The main working materials are in the analytical-modeling repository:
- Repository: https://github.com/colbrydi/analytical-modeling
- Focus: Part 2 and the supporting synthetic-data module
The key question is not just whether the code runs, but whether the generated dataset is interpretable. We will ask:
- What stays stable even when noise is added?
- What information is hidden in real data but visible in synthetic data?
- Why does this matter for model checking and model fitting?
Before Next Class
- Review the synthetic-data workflow and note one place where noise changes your interpretation.
- Revisit the repository README and connect this part to the larger analytical-modeling unit.
- Prepare one question about parameter estimation or model trust for the next class.