Testing the limits of past-adapted explanations by post-endpoint randomisation: anticipatory EEG as a worked case

2026-08-12

AI Summary

This study addresses the challenge of distinguishing whether a model’s fit to data stems from genuine signal rather than overfitting or chance. It proposes a Level II-A inference framework that evaluates the sufficiency of explanations based solely on historical information by randomizing delay times after event endpoints are fixed. Innovatively reframing “past-explainable outcomes” from a default assumption into a quantifiable hypothesis, the approach integrates negative control probes, non-compensatory decision rules, post-hoc endpoint randomization, leakage-proof preprocessing, frozen-label blind comparators, subject eligibility verification, and sequential e-value methods. Applied to anticipatory EEG CNV data, the framework establishes bounds for spurious sufficiency on synthetic benchmarks—yielding an allocation-isolation threshold of 15 μV/s and a sequential e-value path threshold of 30 μV/s—thereby enabling conditionally valid rejections or calibrated affirmations.

Abstract

A predictive model can fit its data even when its information set is insufficient; fit alone cannot establish sufficiency. This Perspective introduces Level II-A, a new design-based inference framework to test this distinction, illustrated in anticipatory EEG using contingent negative variation. A pre-event endpoint is committed before the delay to the imperative event is randomised. That later-assigned delay thereby becomes a negative-control probe of whether past-adapted information was sufficient for an already committed result. Under the past-adapted factorisation, accounts using only pre-commitment information cannot systematically order the endpoint by that delay. Leakage-safe preprocessing, a frozen label-blind comparator and retained-sample qualifications carry the exclusion to the confirmatory residual. A qualified material negative ordering supports conditional insufficiency without identifying a mechanism; an adequately sensitive null supports a bounded affirmative conclusion calibrated by the pipeline's false-adequacy rate. A non-compensatory rule separates these from diagnostic failure, selection-limited, opposite-direction and inconclusive outcomes. No human EEG data are analysed. In the synthetic benchmark, grid-based false-adequacy boundaries are $15\,μ\mathrm{V\,s^{-1}}$ for assignment isolation and $30\,μ\mathrm{V\,s^{-1}}$ for the sequential e-value route, in both directions. The design transfers wherever endpoint commitment precedes an exogenous label, probing sufficiency only where a declared alternative predicts ordering by it. It turns "the past explains it" from a working explanatory assumption into a magnitude-qualified, testable claim.

Problem

• predictive sufficiency
• past-adapted explanations
• negative-control probe
• endpoint commitment
• conditional insufficiency

Innovation

• post-endpoint randomisation
• Level II-A inference
• anticipatory EEG
• negative-control probe
• false-adequacy rate