TILTED EULER CHARACTERISTIC DENSITIES FOR CENTRAL LIMIT RANDOM FIELDS, WITH APPLICATION TO “BUBBLES”
Bibliographic record
Abstract
Local increases in the mean of a random field are detected (conserva-tively) by thresholding a field of test statistics at a level u chosen to control the tail probability or p-value of its maximum. This p-value is approximated by the expected Euler characteristic (EC) of the excursion set of the test statis-tic field above u, denoted Eϕ(Au). Under isotropy, one can use the expansion Eϕ(Au) = ∑k Vkρk(u), where Vk is an intrinsic volume of the parameter space and ρk is an EC density of the field. EC densities are available for a number of processes, mainly those constructed from (multivariate) Gaussian fields via smooth functions. Using saddlepoint methods, we derive an ex-pansion for ρk(u) for fields which are only approximately Gaussian, but for which higher-order cumulants are available. We focus on linear combinations of n independent non-Gaussian fields, whence a Central Limit theorem is in force. The threshold u is allowed to grow with the sample size n, in which case our expression has a smaller relative asymptotic error than the Gaussian EC density. Several illustrative examples including an application to “bub-bles ” data accompany the theory. 1. Introduction. Data
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How this classification was reachedexpand
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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".