The DCA long-range epistasis gap and the IB compression-phase debate are both estimand-vs-estimator stories, but the gap lives in opposite places

Seek's semantic index flagged claim-pdz-dca-couplings-track-short-range-epistasis-more-than-long-range and claim-ib-compression-may-be-a-binning-artifact-not-real-mutual-information as unlinked neighbors (cosine 0.75) sharing surface vocabulary — both describe a gap between a measured quantity and a real one that might be artifact rather than substance. Biostatistics has a standing distinction for exactly this question: whether a discrepancy lives in the estimand (the true target quantity) or the estimator (the procedure used to measure it). Applied to both cases, the resemblance turns out to be a real structural bridge that resolves in opposite directions.

On the DCA side, claim-dca-underestimates-long-range-epistasis-in-allosteric-materials's synthetic-network result and claim-pdz-dca-couplings-track-short-range-epistasis-more-than-long-range's real-protein confirmation (ρ=0.69 short-range vs. ρ=0.48 long-range) both show the same short/long asymmetry, one in a fully controlled ground-truth model and one in measured data — evidence that the estimand (real epistasis) is well-behaved and the gap sits in the estimator (pairwise DCA couplings), which is genuinely under-expressive for long-range, collective coupling. claim-dca-strongest-couplings-only-weakly-influenced-by-phylogenetic-bias closes off the most obvious rival explanation: if phylogenetic sampling bias explained the long-range weakness, correcting it should recover the missing signal, but Rodriguez Horta & Weigt (2021) find the strongest couplings — including the strong long-range ones — are already largely phylogeny-clean. The estimator's long-range blindness looks structural, not a fixable sampling artifact.

On the IB side, Goldfeld et al. prove the opposite structure: in deterministic networks with strictly monotone nonlinearities, the true mutual information is the estimand, and it is mathematically frozen — infinite or constant, unable to fluctuate at all. Any movement the binning estimator reports there is artifact by construction, not a real information-theoretic change; see claim-ib-compression-phase-is-nonlinearity-dependent-not-universal for the separate, already-vaulted line of evidence that the compression phenomenon itself is nonlinearity-dependent rather than universal.

The two fields ask the same diagnostic question — is the gap in the target or the tool? — and answer it oppositely: DCA's gap is estimator-side and real (a genuine representational limit); IB's compression, in the deterministic regime, is estimand-side and provably artifactual. Concept anchors: entity-direct-coupling-analysis, entity-information-bottleneck, entity-estimand, entity-martin-weigt.