Scope And Alternatives
ScientificFitting is a frequentist fitting package for measured data with explicit uncertainty models.
Not Implemented
| Task | Status | Use instead |
|---|---|---|
| Posterior sampling, credible intervals | out of scope | Turing.jl; a ScientificFitting likelihood can be reused there via the external-likelihood interface |
| ODE/PDE parameter estimation | out of scope | SciML (DiffEqParamEstim, SciMLSensitivity) |
| Robust M-estimators (Huber, Tukey) | not implemented | model heavy tails explicitly with fit_likelihood_model (for example Laplace or Student-t errors), which keeps the likelihood interpretable |
| Multidimensional x (surfaces, fields) | not implemented | fit_indexed_model fits observations indexed 1..n that have no meaningful x coordinate; general regression on multidimensional x needs another tool |
| Errors-in-variables beyond linearization | not implemented | the effective-variance propagation assumes small x errors and smooth models; latent-variable EIV needs an explicit model, for example in Turing.jl |
| Global optimization guarantees | out of scope | all solvers are local; multistart and explicit initial_guesses mitigate, not guarantee |
| Effect-size or hypothesis-testing frameworks | out of scope | HypothesisTests.jl |
When A Simpler Tool Suffices
For unweighted or diagonally weighted least squares without diagnostics, LsqFit.jl (which powers this package's fast path) or CurveFit.jl are smaller dependencies. Use ScientificFitting when uncertainties are part of the question: correlated or x errors, count likelihoods, priors, profile intervals, and reviewable diagnostics.
Known Approximations
- Effective variance for x errors is a first-order linearization; its determinant term makes results differ slightly but reproducibly from ODR-convention tools (details).
- Local covariance is curvature at one point; profiles exist because it can fail (details).
- Wilks thresholds for profiles and contours are asymptotic; non-regular problems need simulation (details).
- Prediction and confidence bands are pointwise intervals (68.27% at the default
nsigma=1) under approximate normality of the estimator, not simultaneous bands.