Alternatives to the Chi-Square Test for Evaluating Rank Histograms from Ensemble Forecasts
Bibliographic record
Abstract
Abstract Rank histograms are a commonly used tool for evaluating an ensemble forecasting system’s performance. Because the sample size is finite, the rank histogram is subject to statistical fluctuations, so a goodness-of-fit (GOF) test is employed to determine if the rank histogram is uniform to within some statistical certainty. Most often, the χ2 test is used to test whether the rank histogram is indistinguishable from a discrete uniform distribution. However, the χ2 test is insensitive to order and so suffers from troubling deficiencies that may render it unsuitable for rank histogram evaluation. As shown by examples in this paper, more powerful tests, suitable for small sample sizes, and very sensitive to the particular deficiencies that appear in rank histograms are available from the order-dependent Cramér–von Mises family of statistics, in particular, the Watson and Anderson–Darling statistics.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.039 | 0.284 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.007 | 0.007 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.008 | 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".