Multiscale Statistical Models for Hierarchical Spatial Aggregation
Bibliographic record
Abstract
Scale dependency is an inherent property of geographic phenomena since most geographic patterns under observation vary with scale. Across numerous disciplines, including geography, various types of so‐called “multiscale” models have been used for the task of modeling and understanding the effects of scale. However, most of these models are descriptive—as opposed to inferential—in nature, and few of them (particularly outside geography) are well adapted to the wide variety of data structures typically encountered in geography. In this paper, we introduce a new, general framework for multiscale statistical modeling and inference that is explicitly designed for a broad class of geographic data. The key structural assumption underlying these models is that of a set of hierarchically defined partitions, corresponding to successive aggregations of an initial data space. Within our framework the effects of scale associated with such aggregation are captured through a fundamental decomposition of the data likelihood, directly induced by the hierarchical nature of the partitions, into individual components of local information at all possible spatial resolutions. Upon combining these multiscale likelihoods with an appropriately defined Bayesian prior probability structure, a powerful inferential framework results. We describe in detail how this framework may be used for the tasks of statistical estimation and classification, and illustrate its usage with an analysis of data from census geography.
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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 | 0.006 | 0.021 |
| 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 | 0.003 |
| Scholarly communication | 0.002 | 0.004 |
| 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".