Nonparametric random fields with applications in functional imaging
Bibliographic record
Abstract
In functional imaging, we are searching for the location of a particular effect in a group of images. It is often of interest to perform a statistical test at each point of the image, and reject the null hypothesis of "no effect" where there is significant evidence to do so. For such purpose, a test statistic should be evaluated at each point of the image, resulting in a test statistic image. The test statistic image can be considered as a stochastic process or a random field, f, defined on some parameter space, T, and taking values in R. When the statistic image, f, is submitted to a threshold of level u the p-value will be the excursion probability. When f satisfies certain conditions, Random Field Theory (RFT) can be used to estimate the above excursion probability by calculating the expected Euler characteristic (EC) of the excursion sets of f. The existing RFT results give explicit formulas for E[EC(Au)] when f is a function of Gaussian random fields [26, 27]. From the "hypothesis testing" point of view, this means that the test performed at each point of the image should be parametric. Parametric tests often assume that the observations are normally distributed and this assumption does not always hold. If this normality assumption fails, the underlying random fields of our test will not be Gaussian, and consequently, the Gaussian RFT results would not be valid.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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".