Geostatistical analysis of spatially dependent functional data: Universal Kriging in a Hilbert space
Bibliographic record
Abstract
When dealing with high-dimensional georeferenced data, the need of spatial predictions often results in both theoretical and practical issues. In this work, we address this problem by proposing an extension of some geostatistical techniques to nonstationary functional random fields.\n \nA new theoretical framework is established in order to perform Universal Kriging of spatially dependent functional data belonging to a Hilbert space; moreover, estimators for the spatial mean and the spatial covariance structure are derived.\n \nThanks to the generality of the proposed approach, not only the pointwise but also the differential information brought by the data can be exploited by embedding the analysis in a proper Hilbert space, possibly other than L2, such as a Sobolev space. Nevertheless, the non-stationary approach allows to model the spatial mean through a georeferenced external drift or to include cluster-varying spatial mean models.\n \nProper algorithms to deal with real data are proposed and their performance is tested through an extensive simulation study.\nFinally, the proposed method is applied to daily mean temperature curves recorded in 35 meteorological stations located in Canada’s Maritime Provinces.\n
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| 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 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".