Choose a workflow¶
Choose the statistical model before choosing the uncertainty calculation. Every function accepts ordinary NumPy-compatible arrays, but a covariance matrix alone cannot tell you where it came from.
| Question | Feature | Assumption to check |
|---|---|---|
| How uncertain is the mean curve? | generate_error_bands |
Local Delta approximation; compatible covariance, reference law and fitting dof. |
| Where might one new observation fall? | generate_error_bands |
Independent future noise; explicitly supplied for known/heteroscedastic errors. |
| How do regular response-only models compare? | audit_fit |
Same observations/units, Gaussian likelihood and maximum-likelihood estimates. |
| What does a parameter table say? | fit_summary |
Approximate Student-t/Wald tests of zero parameters, using N-p. |
| Are parameter errors asymmetric? | profile_likelihood_errors |
Regular profile/Wilks calibration and successful local nuisance reoptimization. |
| How variable are empirical refits? | bootstrap_curve_fit |
IID observation errors, adequate mean model, fixed predictors; inspect failed attempts. |
| Which parameters are locally correlated? | collinearity_diagnostics |
Local covariance-based evidence, not structural identifiability. |
| What covariance is available at a bound? | robust_bounded_pcov |
Active parameters held fixed; only the free block has conditional covariance. |
| How uncertain is a derived quantity? | propagate_uncertainty |
Gaussian local parameter approximation; domain validity and finite moments. |
| Can experiments share parameters? | GlobalFitGroup |
One joint residual model and one common unknown scale when relative weighting is used. |
| Are both axes measured with error? | eiv_curve_fit |
Independent scalar/vector axis errors, ODR covariance and supported SciPy backend. |
A useful starting sequence¶
- Fit the appropriate response-only, joint or EIV model.
- Inspect convergence, model adequacy, numerical rank and constraint activity.
- Retain the noise/covariance convention and residual degrees of freedom.
- Choose an interval or propagation method whose assumptions match that fit.
- Inspect diagnostics and uncertainty failures before interpreting results.
Covariance is not interchangeable metadata
EIV covariance does not make a vertical-response likelihood audit an ODR likelihood. Bootstrap covariance does not establish a Student-t pivot. Conditional covariance at a bound is not unrestricted marginal uncertainty.
See integration guidance for valid projections between modules, the concepts guide for equations and limitations, and executable examples for reproducible complete workflows.