Urban scaling with censored data
Bibliographic record
Abstract
In the realm of urban science, scaling laws are essential for understanding the relationship between city population and urban features, such as socioeconomic outputs. Ideally, these laws would be based on complete datasets; however, researchers often face challenges related to data availability and reporting practices, resulting in datasets that include only the highest observations of the urban features (top- k ). A key question that emerges is: Under what conditions can an analysis based solely on top- k observations accurately determine whether a scaling relationship is truly superlinear or sublinear? To address this question, we conduct a numerical study that explores how relying exclusively on reported values can lead to erroneous conclusions, revealing a selection bias that favors sublinear over superlinear scaling. In response, we develop a method that provides robust estimates of the minimum and maximum potential scaling exponents when only top- k observations are available. We apply this method to two case studies involving firearm violence, a domain notorious for its suppressed datasets, and we demonstrate how this approach offers a reliable framework for analyzing scaling relationships with censored data.
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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 | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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".