Decay fitting with local intervals

MODEL "Decay fitting with local intervals"
DESCRIPTION "Inspect approximate parameter intervals under independent equal-variance error assumptions."
TAGS "chemistry", "curve-fitting", "uncertainty"

# Synthetic exponential-decay calibration with local parameter intervals.
# This exact calculation is retained in the independent-reference QA.
# x uses an arbitrary consistent time unit; response uses signal units.
# Amplitude and baseline use signal units; rate uses inverse time units.
# Independent normal errors, equal unknown variance estimated from residuals.
# Intervals are individual local approximations, not prediction intervals.
# Inspect Report to see estimates, bounds, residuals, rank and stopping reason.
# Weak identification/nonlinearity can cause poor coverage despite finite bounds.

Report = CURVE_FIT.REPORT(
  (time, amplitude, rate, baseline) => amplitude*EXP(-rate*time)+baseline,
  [0.0,0.2,0.5,1.0,1.5,2.0,3.0,4.0,5.0,6.0],
  [2.7199999999999998,2.356459764957134,2.001251415324912,1.5168047290993827,1.119850597866773,0.9068327134598556,0.5838954278071566,0.45094415030052315,0.3574737202135644,0.3459893843691465],
  [1.0,1.0,0.0], 1e-12, 1000,
  {uncertainty: "local_iid", confidence: 0.95}
)
END MODEL