Uncertainty¶

Fitting produces not just parameter values but a covariance. esf can capture it and propagate it through a simulation as quantile bands. Uncertainty is opt-in — the simulators stay float-only and are never slowed down by it.

Design and scope are in development/uncertainty-propagation-design.md.

Capture (Tier 0)¶

Every fit exposes the fitted covariance over its varying parameters, keyed by ESFParams attribute name:

fit = esf.temperature_stress_factor_fit(prms, rates, apply=False)
unc = fit.parameter_uncertainty()      # a ParameterUncertainty
unc.report()                           # value, std, relative std per parameter

Propagate (Tier 1)¶

ParameterEnsemble samples the covariance (jointly, respecting within-fit correlations; out-of-bounds samples are rejected and redrawn) to produce ESFParams copies. simulate_with_uncertainty runs any simulation function over the ensemble and returns quantile bands.

import esf

band = esf.simulate_with_uncertainty(
    simulate_fn,          # e.g. a drive-cycle simulation returning a frame
    uncertainty,          # a ParameterUncertainty (possibly merged across fits)
    prms,
    n=1000,               # ensemble size (use ~100 for expensive DST runs)
)

The result carries the median and the requested quantile bands over the simulated quantity, which you can plot as a shaded region.

Scope¶

• The covariance is block-diagonal across fit stages — separate fits are treated as independent (captures within-stage correlations, e.g. the three k_*_dod together, but not cross-stage correlation from freezing earlier parameters).
• Only fit covariance is modelled so far; per-point measurement noise and a full pipeline bootstrap (Tier 2) are planned.

See the public API for ParameterUncertainty / ParameterEnsemble / simulate_with_uncertainty.