docs: correct skyline quadrature self-consistency claim - #868
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ivan-aksamentov wants to merge 1 commit into
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docs: correct skyline quadrature self-consistency claim#868ivan-aksamentov wants to merge 1 commit into
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The quadrature issue claimed the midpoint rule is exact for the piecewise-constant skyline with no quadrature error. That holds only if the demographic function is the midpoint-snapped one. For the reported merger-time-midpoint boundaries the rule is self-consistent, not exact: exact on lineage-count intervals with no skyline boundary, with a bounded straddle error on the up-to n_points-1 intervals crossing a boundary. Record the off-grid error characterization.
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We might want to replace this midpoint business. I'll look into it. |
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docs/coalescent-skyline-quadrature-contract->rustUpdate:
kb/issues/N-coalescent-skyline-quadrature-contract-undecided.md: replace the "no quadrature error" claim with self-consistency and record the off-grid error bound
Follow-up to: Feat/exact skyline #856
The quadrature issue claimed the midpoint rule is exact for the piecewise-constant skyline, with no quadrature error. That holds only if the operative demographic function is taken to be the midpoint-snapped one. For the merger-time-midpoint boundaries the tool actually reports, the rule is self-consistent, not exact.
This corrects the wording to self-consistency and records the off-grid error characterization: the midpoint rule is exact on every lineage-count interval that contains no skyline boundary, while at most$n-1$ intervals straddle a boundary and each contributes an error bounded by its exposure times the inter-segment $T_c$ contrast [src].
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