Spectral methods for non-linear co-regionalization
Bibliographic record
Abstract
It is frequently the case that direct and indirect measurements have to be combined to deliver meaningful estimates of the variable of interest. Linear co-regionalization, which assumes that all variables share common spatial structures, has widely been used in geostatistics to model the correlated spatial random fields. The underlying linearity assumption, however, is restrictive with respect to the choice of the direct and cross variograms, as it assumes very similar spatial structure for the direct and indirect variables. In this contribution, a new method of non-linear co-regionalization based on Fourier transformation is presented. First, the coherence of the corresponding fields based on their power spectra is introduced. The coherence gives a variogram-dependent upper and lower limit for the correlation of the random fields. The direct variograms of the two fields depend on their phase spectrum. The phase differences of these phase spectra determine the cross-variogram. A simulation method for generating correlated random fields with given direct and cross variograms is presented. The method allows the use of different models for the direct variograms as well as for the cross variogram. Further, the method enables the consideration of non-Gaussian copula-based spatial features, such as different types of spatial asymmetries. This enables the simulation of correlated fields with value-dependent correlations. A real world and various theoretical examples with different Gaussian and non-Gaussian copula-based dependence structures will be used to illustrate the methodology and its flexibility.
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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 | 0.004 | 0.011 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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".