Maxima of discretely sampled random fields, with an application to 'bubbles'
Why this work is in the frame
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Bibliographic record
Abstract
A smooth Gaussian random field with zero mean and unit variance is sampled on a discrete lattice, and we are interested in the exceedance probability or P-value of the maximum in a finite region. If the random field is smooth relative to the mesh size, then the P-value can be well approximated by results for the continuously sampled smooth random field (Adler, 1981; Worsley, 1995a; Taylor & Adler, 2003; Adler & Taylor, 2007). If the random field is not smooth, so that adjacent lattice values are nearly independent, then the usual Bonferroni bound is very accurate. The purpose of this paper is to bridge the gap between the two, and derive a simple, accurate upper bound for intermediate mesh sizes. The result uses a new improved Bonferroni-type bound based on discrete local maxima. We give an application to the ‘bubbles’ technique for detecting areas of the face used to discriminate fear from happiness.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.010 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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 it