3. Covariance convention

Status: accepted · 2026-10-22

Context. Whether the parameter covariance is scaled by χ²/ndf (absolute_sigma in curve_fit, scale_covar in lmfit) changes every reported uncertainty. The library defaults differ, and most users are not aware of the choice.

Decision.

• With yerr, the errors are absolute 1σ uncertainties and the covariance is not scaled. χ²/ndf is reported as a consistency check, with a warning if it is implausible.

• Without yerr, the noise level is estimated from the residuals and the covariance is scaled. The report says so explicitly and shows the RMSE instead of χ²/ndf.

• scale_covar=True/False overrides the default. The choice is stored in the result and shown in the report.

Consequences. Users who supply measured uncertainties get the physically expected behaviour. Results can differ from lmfit’s default (which always scales) when yerr is given. The documentation explains this difference, and the reference tests cover both modes.