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The tolerance ε is required to be nonnegative because it thresholds a nonnegative distance. A value of zero tests any strictly positive discrepancy, whereas a positive value filters changes smaller than the chosen scale. The value should be set with reference to numerical precision and measurement noise.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| epsilon | Distance threshold |
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Original context
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Marker status and causal status are separate. A declaration might reveal an emerging organization without causing it. The stronger claim is that the declaration reenters processing and contributes to subsequent change. Prediction can support the marker claim. An intervention on the feedback channel is needed to assess the causal extension.
2.3. Independent onset, persistence, and detection delay
For tolerance ϵ≥0 and a window of W consecutive updates, let TW contain every candidate starting time for which the required measurements are available. Eligibility is determined without reference to declaration time. Define
Pt(ϵ,W)=1{min0≤j<Wδt+j>ϵ},
tΔ(ϵ,W)=inf{t∈TW:Pt(ϵ,W)=1}.
(2.4)Exact original notation
ϵ\ge 0