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

Technical Summary: Testing the Limits of Past-Adapted Explanations by Post-Endpoint Randomisation

Problem Statement
In anticipatory neuroscience, particularly regarding EEG signals like the Contingent Negative Variation (CNV), researchers typically explain pre-event brain activity using "past-adapted" information: elapsed time, cue probability, conditional hazard, arousal, and trial history available before the event occurs. While predictive models can fit data using these factors, a "fit" does not establish "sufficiency." The core problem is distinguishing whether these past-adapted factors exhaust the systematic variation in a committed endpoint or if unexplained systematic variation remains that might be ordered by information not yet available at the time of the measurement. Standard goodness-of-fit measures cannot resolve this; they leave open the possibility that the past explains the data merely by chance or overfitting, without proving that no future-dependent information is required.

Methodology: Level II-A Design-Based Inference
The paper introduces Level II-A, a design-based inference framework that tests the distinction between fit and sufficiency using post-endpoint randomisation. The methodology relies on a strict temporal boundary and a series of operational and statistical conditions:

1. Endpoint Commitment: A single-trial endpoint (e.g., a CNV-like amplitude) is computed and "locked" at time $t_1$ using only information available up to that moment ($F_{t_1}$). This includes the use of a "forward-only" comparator (a label-blind predictor) to remove recorded anticipatory structure, leaving a "frozen residual."
2. Post-Commitment Randomisation: Only after the endpoint is fixed does the system assign a delay ($\tau_L$) to the imperative event. This delay is drawn from a declared randomisation law based on pre-assignment strata but is strictly concealed from the endpoint construction and comparator fitting.
3. The Null Hypothesis: Under the "past-adapted factorisation," the assigned delay (a future label) should be statistically independent of the already committed endpoint or frozen residual. Formally, $P(\tau_L \in D | F_{t_1}) = P_{sch}(D | R_j)$. If the past-adapted class is sufficient, the assigned delay cannot systematically order the endpoint.
4. Conditions for Validity: The framework requires:
   • (R1) Operational Scheduler: The delay is generated and concealed after commitment.
   • (R2) Temporal Integrity: No post-$t_1$ data (e.g., zero-phase filtering) leaks into the endpoint or comparator.
   • (R3) Retained-Sample Integrity: Selection processes (delivery, artefact rejection, inclusion) must not induce a dependency between the delay and the endpoint (delay-neutrality).
5. Decision Architecture: The classifier is non-compensatory and follows a strict hierarchy:
   • Audits: Checks for temporal leakage, delivery compliance, and scheduler integrity.
   • Qualifications: Checks for selection bias (collider diagnostics), participant estimability, and route validity (assignment-isolation vs. sequential e-value).
   • Inference: Tests for a material negative slope ($\beta_\tau < 0$) using route-specific calibration (randomisation tests or martingale e-values) and a magnitude threshold ($\beta_{min}$) derived from a label-blind resolution floor.
   • Outcomes: The system classifies results into: Supported Negative Departure (evidence of insufficiency), Forward-Only Adequate (affirmative null), Diagnostic Failure, Selection-Limited, Opposite-Direction, or Inconclusive.

Key Contributions

• Level II-A Framework: A new inferential structure that transforms the assumption "the past explains it" into a testable, magnitude-qualified claim. It shifts the burden of proof from "showing a fit" to "ruling out future-dependent ordering."
• Post-Endpoint Randomisation Probe: The use of a delay assigned after the measurement as a negative control. This creates a "boundary test" where any systematic ordering by the delay implies a failure of the past-adapted class.
• Magnitude-Qualified Affirmative Null: The paper defines a "forward-only adequate" outcome not as a simple non-rejection, but as a bounded conclusion. It requires that the analysis pipeline is sensitive enough to detect a specific magnitude of effect (determined by simulation-calibrated false-adequacy rates) and finds none.
• Synthetic Benchmarking: The authors provide a fully specified, open-source benchmark pipeline (Level II-A post-endpoint randomisation benchmark) with 1200 simulated datasets per scenario. This validates the pipeline's ability to control false support, recover injected signals, and correctly identify operational failures (leakage, selection bias, collider effects).

Results
The paper presents results exclusively from synthetic data; no human EEG data are analyzed. The synthetic benchmark validates the pipeline against seven scenario families:

• Clean Null: Under a pure forward-only generator, the pipeline produced 0/1200 supported outcomes (false support rate = 0.000). It classified 89.4% as "Forward-Only Adequate" and 9.8% as "Inconclusive" (due to resolution limits), demonstrating strict control of false positives while acknowledging information costs.
• Injected Signal: When a material negative slope ($-60 \mu V s^{-1}$) was injected, the pipeline supported it in 99.1% of cases with 0% false-adequacy outcomes.
• Failure Modes:
  • Temporal Leakage: 100% of datasets with post-endpoint leakage were correctly classified as "Diagnostic Failure."
  • Selection Bias: Scenarios with standard selection or collider-induced bias were correctly routed to "Selection-Limited" outcomes (99.7% and 99.9% respectively), preventing false support.
  • Opposite Direction: Positive injections were correctly classified as "Opposite-Direction Departures" (99.3%), blocking them from being interpreted as support for the negative hypothesis.
• Resolution Boundaries: The benchmark established false-adequacy boundaries for the affirmative null: 15 $\mu V s^{-1}$ for the assignment-isolation route and 30 $\mu V s^{-1}$ for the sequential e-value route. Below these magnitudes, the pipeline cannot reliably distinguish a clean null from a small systematic departure.

Significance and Claims
The paper claims to provide a methodological boundary rather than a biological discovery. Its significance lies in:

1. Rigorous Exclusion: It offers a way to test whether a class of past-adapted models is sufficient to explain a committed endpoint, moving beyond mere model fitting.
2. Mechanism Neutrality: A "Supported Negative Departure" indicates that the past-adapted class is insufficient but does not identify the mechanism (e.g., it does not prove "precognition" or a specific physical substrate). It simply establishes that the declared past-adapted factors do not exhaust the variation.
3. Calibrated Nulls: It provides a framework for "evidence of absence" that is calibrated by the pipeline's sensitivity (false-adequacy rate), turning the "absence of evidence" into a "bounded affirmative conclusion."
4. Generalizability: While illustrated with anticipatory EEG, the authors state the design is domain-general, applicable to any scenario where a statistic is irrevocably committed before an exogenous label is generated (e.g., forecasting, clinical trials, algorithmic decision systems).

The authors explicitly state that no empirical decision is made in this paper; the work fixes the rule by which such decisions could be made and demonstrates via synthetic data that the rule behaves as declared. The framework requires independent replication (Level II-B) to move from a class-level rejection to a substantive mechanistic theory.