On the properties of some nonparametric concordance measures in the discrete case
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Bibliographic record
Abstract
It is shown here that Kendall's τ and Spearman's ρ are monotone with respect to the concordance ordering of pairs of discrete as well as continuous random variables. This extends and completes results of [Tchen, A.H., 1980, The Annals of Probability, 8, 814–827.] It is also shown that various relationships between Kendall's τ and Spearman's ρ mentioned in [Nelsen, R.B., 1999, An Introduction to Copulas. Lecture Notes in Statistics no. 139 (New York: Springer).] remain valid for discrete variables. In particular, a result of [Capéraà, P. and Genest, C., 1993, Journal of Nonparametric Statistics, 2, 183–194.] is extended to the case of discrete random pairs. Finally, an analytic expression is given for the most extreme values of Kendall's τ and Spearman's ρ associated with discrete uniform variates.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.012 | 0.053 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.004 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it