What does a twin get wrong when its gain is fitted from a noisy logged input, and does more data fix it?

research/eiv-twin

A twin gain fitted from a noisy logged input is attenuated by exactly the reliability ratio λ (0.800 vs 0.802 simulated), more data makes the twin's own 95% interval worse (covers the true gain 53%→0% for n=20→200) with no residual warning, a feedforward controller overshoots by exactly 1/λ, and known-noise or instrument repairs cost variance and fail at small n.

5 tests

What it found

Regressing the plant output on a logged input that carries sensor noise attenuates the fitted gain by the reliability ratio λ = σ_u²/(σ_u²+σ_v²) exactly (0.800 vs 0.802 simulated at λ=0.8). It is bias, not variance, so more data makes it worse: the twin's own 95% interval covers the true gain 53% / 15% / 0% at n=20 / 50 / 200 while covering the attenuated value 94–97%, and the twin's fit residuals are exactly uncorrelated with its regressor, so nothing warns. A feedforward controller built on it overshoots the real plant by exactly 1/λ (1.25× at λ=0.8, 2× at 0.5). A known-noise correction or a second independent measurement as instrument removes the bias (RMSE 0.20 to 0.02–0.05 at n=200–1000), but a 20% misjudged noise variance leaves a ±5% bias and at n=20 with λ=0.5 the repairs are far worse than the biased fit. Stylised: scalar Gaussian plant, simulated “real” system.

A figure from its own output

Figure produced by research/eiv-twin: coverage — eiv-twin/experiments/coverage.svg, written by the project's own experiment code.

Paper, code and results

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Produced with AI assistance (Claude). Results are from the code in this repository and are simulated or stylised unless the abstract says otherwise; nothing here implies affiliation with or endorsement by any lab, researcher or company cited. MIT licensed.