Efficient computation on large regular grids of higher-order spatial statistics via fast Fourier transform
Bibliographic record
Abstract
The complex spatial structures of natural variables are often caused by geological, physicochemical, meteorological, and biological processes that have shaped the emergence of the fields. The typical prediction of the spatial distributions of these phenomena is based on second-order geostatistical models. However, this approach has limitations, given the high complexity, non-Gaussian distributions, and nonlinear spatial connectivity models inherent in geological systems. Recently, researchers have suggested using higher-order spatial statistics, based on two- and three-point spatial statistics, to better capture spatial phenomena. Nevertheless, applying these methods requires intense numerical calculations, particularly in the case of extensive geostatistical models, and becomes especially intricate when utilized for conditioning realizations, such as in inverse problems. Spatial asymmetries and higher-order spatial cumulants, as well as their generalizations, are important higher-order statistics for characterizing non-Gaussian features. In this study, we focus on third-order statistics derived from two- and three-point spatial statistics. A MATLAB program has been developed to compute efficiently these spatial statistics using the FFT algorithm. The overall approach of these programs draws inspiration from the method successfully used for the fast calculation of variograms and cross-covariances using FFT. We recall the methodology associated with the computation of direct- and cross-variograms using FFT, as well as transiograms for categorical data. Codes are created to process regular grid data, whether it is complete or incomplete. Post-processing tools have been added to help geomodelers visualize the results. Using the FFT method is faster and delivers the same results as conventional spatial methods for this type of data. These programs are particularly valuable tools for geostatistical modeling and estimation when higher-order statistics are present in the spatial structures of natural variables, providing an efficient solution to the computational challenges associated with such applications. • The FFT-based method is extended to compute higher-order spatial statistics. • Two-point asymmetry functions are developed using FFT. • The MATLAB code is applicable to both continuous and categorical cases. • The program works in d -dimensions with non-collocated data; • A post-processing function is developed to compute experimental spatial statistics.
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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 | 0.001 |
| 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".