Experimental cosmic statistics - II. Distribution
Bibliographic record
Abstract
Colombi et al. (Paper I) investigated the counts-in-cells statistics and their respective errors in the τCDM Virgo Hubble Volume simulation. This extremely large N-body experiment also allows a numerical investigation of the cosmic distribution function, ϒ (Ã), itself for the first time. For a statistic A, ϒ (Ã) is the probability density of measuring the value à in a finite galaxy catalogue. ϒ was evaluated for the distribution of counts-in-cells, PN, the factorial moments, Fk, and the cumulants, ξ̄ and SNs, using the same subsamples as Paper I. While Paper I concentrated on the first two moments of ϒ, i.e. the mean, the cosmic error and the cross-correlations, here the function ϒ is studied in its full generality, including a preliminary analysis of joint distributions ϒ (Ã,B̃). The most significant, and reassuring result for the analyses of future galaxy data is that the cosmic distribution function is nearly Gaussian provided its variance is small. A good practical criterion for the relative cosmic error is that ΔAA≲0.2. This means that for accurate measurements, the theory of the cosmic errors, presented by Szapudi & Colombi and Szapudi, Colombi & Bernardeau, and confirmed empirically by Paper I, is sufficient for a full statistical description and thus for a maximum likelihood rating of models. As the cosmic error increases, the cosmic distribution function ϒ becomes increasingly skewed and is well described by a generalization of the lognormal distribution. The cosmic skewness is introduced as an additional free parameter. The deviation from Gaussianity of ϒ(F̃k) and ϒ(S̃ N) increases with order k, N and similarly for ϒ(P̃ N) when N is far from the maximum of PN, or when the scale approaches the size of the catalogue. For our particular experiment, ϒ(F̃k) and ϒ(ξ ̄ ̃) are well approximated with the standard lognormal distribution, as evidenced by both the distribution itself and the comparison of the measured skewness with that of the lognormal distribution.
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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 | 0.009 | 0.044 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 0.002 |
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".