One long twin run or many replications when every run starts in the wrong state?

research/replicate-twin

One long twin run or many replications under a start-up transient: exact AR(1) MSE and t-interval coverage (single run minimises MSE; replication costs 1.07×–2.2×; 92% coverage at MSE-optimal deletion for short replications), batch means not worse, preliminary M/M/1 coverage 6–84%.

9 tests

What it found

Splitting a fixed budget of N twin draws into r replications, each started at an offset and with d draws deleted, gives iid replication means, but the warm-up bias does not shrink with r. For an AR(1) the MSE and the exact coverage of the Student-t interval are closed-form (0.921 vs 0.921 simulated at r=50): a single run minimises MSE, replication costs at most 1.07× at φ=0.9 but 2.2× at φ=0.99, and the nominal-95% interval covers 92% at the MSE-optimal deletion once replications are short (no deletion reaches 94% at 40 draws each). Single-run batch means were not worse in this model. Preliminary M/M/1 simulation: 30 short replications cover 5.8% of the time, and no setting tried reaches 95%. Stylised: Gaussian AR(1), one start offset, simulated “real” system.

A figure from its own output

Figure produced by research/replicate-twin: mse_ratio — replicate-twin/experiments/mse_ratio.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.