Applied mathematics - Experimental inference

MODEL "Applied mathematics - Experimental inference"
DESCRIPTION "Synthetic exponential decay with residuals and optional local IID parameter uncertainty."
TAGS "applied-mathematics", "inference", "scenarios"

# Controls: changing confidence changes intervals, not the observations.
input Confidence = 0.95
  VALIDATE BETWEEN 0.5 AND 0.9999
input InitialRate = 0.5
  VALIDATE BETWEEN 0.0001 AND 100

# Synthetic observations in consistent time and signal units.
Times = [0,0.5,1,1.5,2,3,4,5]
Observations = [3.43,2.5,1.91,1.43,1.17,0.78,0.59,0.49]
output Fit = CURVE_FIT.REPORT(
  (time, amplitude, rate, baseline) => amplitude * EXP(-rate * time) + baseline,
  Times, Observations, [3,InitialRate,0.4], 1e-12, 1000,
  {uncertainty: "local_iid", confidence: Confidence}
)

# Inspect Fit for completion, residuals, rank and interval assumptions.
output Parameters = Fit.parameters
output Assumptions = "Independent errors with equal unknown variance; individual local parameter intervals, not prediction intervals. Weak identification can undermine coverage."

END MODEL