Two-point Statistics without Bins: A Continuous-function Generalization of the Correlation Function Estimator for Large-scale Structure
Bibliographic record
Abstract
Abstract The two-point correlation function (2pcf) is the key statistic in structure formation; it measures the clustering of galaxies or other density field tracers. Estimators of the 2pcf, including the standard Landy–Szalay (LS) estimator, evaluate the 2pcf in hard-edged separation bins, which is scientifically inappropriate and results in a poor trade-off between bias and variance. We present a new 2pcf estimator, the Continuous-Function Estimator, which generalizes LS to a continuous representation and obviates binning in separation or any other pair property. Our estimator, inspired by the mathematics of least-squares fitting, replaces binned pair counts with projections onto basis functions; it outputs the best linear combination of basis functions to describe the 2pcf. The choice of basis can take into account the expected form of the 2pcf, as well as its dependence on pair properties other than separation. We show that the Continuous-Function Estimator with a cubic-spline basis better represents the shape of the 2pcf compared to LS. We also estimate directly the baryon acoustic scale, using a small number of physically motivated basis functions. Critically, this leads to a reduction in the number of mock catalogs required for covariance estimation, which is currently the limiting step in many 2pcf analyses. We discuss further applications of the Continuous-Function Estimator, including determination of the dependence of clustering on galaxy properties and searches for potential inhomogeneities or anisotropies in large-scale structure.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.007 | 0.028 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".