Scope: Lectures 03-04 · Purpose: Fit only a common magnitude intercept at fixed LCDM shape using the 18-object teaching excerpt and its aligned covariance block.
Setup and data
- Use `pantheonplus-subset.csv` and `pantheonplus-subset-covariance.csv` only; do not substitute diagonal errors for the covariance.
- Verify the two files have 18 rows, matching CID order, and a positive-definite covariance.
- Treat the redshift-stratified selection as a methods demonstration, not a representative survey sample.
Procedure
- Read data and covariance and assert row counts and order.
- Compute the fiducial model distance modulus for each zHD.
- Construct residual r=mu_obs-mu_model and solve for the GLS constant offset beta.
- Compute sigma_beta=(1^T C^-1 1)^-1/2 using linear solves.
- Calculate residual chi-square before and after fitting beta; state the conditional degrees of freedom.
- Repeat with diagonal errors only as a deliberately flawed comparison and explain the changed result.
Deliverables
Deliver: runnable script, residual plot with units and provenance, beta and uncertainty, covariance checks, and a paragraph forbidding survey-level interpretation.
Assessment criteria
Rubric: row/covariance alignment 25%; correct GLS implementation 25%; uncertainty and residual diagnostics 20%; plot/provenance 15%; limitations 15%.
Uncertainty and interpretation
Report numerical precision, input uncertainty, model assumptions, and covariance availability separately. Label every output as directly measured, published summary, derived, or model/synthetic. A successful script run is not evidence that the scientific interpretation is valid.
Revisions and resubmissions are encouraged. Credit is based on defensible reasoning, validation, provenance, and clear limitations.