Section 3: Fitting Data¶

Building a model is only half the job. The other half is extracting physical parameters from real data by finding the model settings that best describe what was measured. This section introduces the statistical framework behind fitting and applies it first to a simple line, then to the scattering models built in Section 2.

By the end of this section you will be able to:

• Explain what chi-squared minimization does and why it works
• Use scipy.optimize.curve_fit to fit any parametric model to data
• Extract parameter values and their uncertainties from the covariance matrix
• Construct and plot a confidence band around a fitted model
• Read a correlation matrix and understand what high parameter correlation means
• Fit a polydisperse sphere form factor to noisy scattering data using log-scale-weighted residuals

All code belongs in chapter_03_fitting.ipynb. The sphere_form_factor, polydisperse_sphere, and plot_form_factor functions from chapter_02_sphere.ipynb are needed in the third page — copy them into the first cell of this notebook so everything is self-contained.

Pages in this section¶

1. Chi-Squared and Fitting a Line
2. Interpreting the Results
3. Fitting Scattering Data