A Data-Driven Method for Reconstructing a Distribution from a Truncated Sample with an Application to Inferring Car-Sharing Demand
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Bibliographic record
Abstract
This paper proposes a method to recover an unknown probability distribution given a censored or truncated sample from that distribution. The proposed method is a novel and conceptually simple detruncation method based on sampling the observed data according to weights learned by solving a simulation-based optimization problem; this method is especially appropriate in cases where little analytic information is available but the truncation process can be simulated. The proposed method is compared with the ubiquitous maximum likelihood estimation (MLE) method in a variety of synthetic validation experiments, where it is found that the proposed method performs slightly worse than perfectly specified MLE and competitively with slightly misspecified MLE. The practical application of this method is then demonstrated via a pair of case studies in which the proposed detruncation method is used alongside a car-sharing service simulator to estimate demand for round-trip car-sharing services in the Boston and New York metropolitan areas.
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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 | 0.001 | 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 | 0.001 |
| 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 it