How should cheap biased twin samples be weighted against scarce real ones?

research/mix-twin

Mixing cheap biased twin samples with scarce real ones: exact optimal weight, twin worth capped at σ²/δ² real samples, equal pooling helps iff δ²<a+b, and estimating the bias from data is costly (plug-in worse than real-only for large bias).

9 tests

What it found

For a mean estimated from n real and m twin samples with twin bias δ, the optimal weight and MSE are exact and the twin is worth at most σ²/δ² real samples however large m is (e.g. 157.5 of a 160 cap at m=10⁴). Equal-weight pooling beats real-only iff δ² < σ²/n + σ²/m, so more twin data narrows the safe range (3.99× worse than real-only at δ=2√a). Estimating the bias from the data is costly: the plug-in weight is worse than real-only for large bias (peak 1.24×), and a 5% pretest peaks at 2.41×. Stylised: scalar Gaussian, constant bias, no robot data.

A figure from its own output

Figure produced by research/mix-twin: mse_vs_bias — mix-twin/experiments/mse_vs_bias.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.