Uncertainty near nonlinearities and calibration limits
All 25 geometry checks and an independent boundary-distribution control pass. The research tools detect conditions in which ordinary linear uncertainty is incomplete. They do not qualify confidence intervals for the NASA fits or change any existing model preference.
An IMU (inertial measurement unit) measures turning and acceleration. The archive analysis estimates instrument calibration within allowed limits. A fit reaching a limit does not make that parameter known exactly.
What the controls establish
| Example | Result |
|---|---|
| Linear model, interior parameters | The local covariance agrees with the independent analytic answer. |
| Parameter at either limit | It remains in the full derivative/rank calculation; the tool flags incompatibility with ordinary interior Gaussian uncertainty. |
| Quadratic observation | Nonlinear departures are measured in supplied noise units, without rescaling noise to fit residuals. |
| Zero or redundant derivative | No finite parameter covariance is reported for an unidentifiable direction. |
| Two indistinguishable parameter branches | Both are retained; their different future predictions remain visible. |
| Changed parameter units | Rank and physical covariance are preserved. |
| Incomplete nonlinear probes | The tool reports how many parameter directions were examined; passing one direction is not a full nonlinear check. |
The local covariance uses the complete noise-weighted derivative matrix, scaled by the declared parameter ranges. Its provisional relative singular-value cutoff is recorded. An active parameter is never silently removed. The reported covariance is explicitly unconstrained and local: it is not a valid symmetric confidence interval for a fit at a boundary.
Why fixing a parameter at its limit is misleading
In an independently calculated scalar example, observations have unit Gaussian noise and the true parameter is at its lower limit of zero. The fitted parameter is constrained between zero and ten. Half the repeated estimates equal zero; the other half mostly lie above it. Their mean is 0.399 and variance 0.341. Treating the parameter as fixed would assign variance zero. Treating the estimate as an ordinary unconstrained Gaussian would assign variance one. Neither describes this bounded estimator's distribution.
An interior likelihood threshold intended for 95% coverage instead has 97.5% coverage at this example's boundary. These exact toy results explain why the archive's cost contours cannot receive confidence labels without calibration. They are not estimates of NASA instrument errors or NASA interval coverage.
Prediction sensitivity, without invented confidence
A second tool preserves all supplied parameter points whose costs lie within an explicit allowance above the sampled grid minimum. It reports their prediction range, including separated branches. There is no default statistical threshold.
These are sampled sensitivity ranges. A sparse grid does not prove a global optimum, find all branches, or establish continuous prediction extrema. If other parameters were held fixed, the costs are slices, not profiled likelihoods. The tool performs no nuisance optimization and makes no scientific decision.
Next step
The bounded archive-development plan specifies how to use these checks before an observed-data comparison: one shared covariance, training-only estimation, full calibration directions, and explicit nonlinear/boundary treatment. It authorizes no fits. The original studies, uncertainty assumptions and unresolved labels remain unchanged. Covariance-choice sensitivity still does not integrate covariance-parameter uncertainty.
This work makes zero NASA reads, zero observed fit starts and zero native predictions. The boundary calculation is deterministic quadrature, not a simulation campaign. Previous linear prediction controls remain useful where their assumptions hold.
Reproduce
env PYTHONPATH=analysis OPENBLAS_NUM_THREADS=2 OMP_NUM_THREADS=2 MKL_NUM_THREADS=2 ~/venv/bin/python docs/ilvis0-nonlinear-uncertainty-controls-20261012/build_report.py
The receipt hashes the source, tests and report artifacts and records the numerical environment. All controls use small matrices or one-dimensional quadrature.