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A Bayesian Spatial Model to Correct Under-Reporting in Urban Crowdsourcing
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Applies a Bayesian spatial latent-variable (Ising-based) model with heterogeneous reporting rates to correct under-reporting in NYC 311 flood reports, improving prediction of future reports and equity of inspection allocation.
Problem
Urban crowdsourcing reports (e.g., 311 flood reports) are positive-unlabeled: unreported events cannot be distinguished from non-events, and reporting rates vary by demographics, so resource allocation based on reports is biased and inequitable.
Approach
Model latent event occurrence as an Ising model over a spatial network of census tracts, with reports generated from occurrence via a reporting rate that is either constant or a logistic function of demographics; spatial correlation lets the model infer unreported events in PU settings.
Key results
- On semi-synthetic heterogeneous-reporting data, the heterogeneous model reaches AUC 0.642 vs 0.520 homogeneous, 0.513 spatial baseline, 0.501 GP baseline for recovering latent flood states.
- On Hurricane Ida test-period reports, heterogeneous reporting model achieves AUC 0.680 and RMSE 0.355, vs GP baseline AUC 0.629 and RMSE 0.417; its AUC gain over the GP baseline is 0.051 (p=0.003).
- Pooled across three storms, reporting rates are higher in census tracts with higher population, higher white proportion, and higher owner-occupied household share; spatial correlation theta_1 estimated at 0.15 (95% CI 0.08-0.21) for Ida.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use heterogeneous rather than homogeneous reporting rates | Bayesian spatial model · Semi-synthetic, heterogeneous reporting | AUC: 0.520 -> 0.642; 0.123 | Helped |
| Use heterogeneous reporting rates rather than the GP baseline | Bayesian spatial model · Semi-synthetic, heterogeneous reporting | AUC: 0.501 -> 0.642; 0.142 | Helped |
| Use heterogeneous reporting rates rather than the spatial baseline | Bayesian spatial model · Semi-synthetic, heterogeneous reporting | AUC: 0.513 -> 0.642; 0.129 | Helped |
| Model constant reporting rates rather than use the GP baseline | Bayesian spatial model · Semi-synthetic, homogeneous reporting | AUC: 0.536 -> 0.577; 0.041 | Helped |
| Model constant reporting rates rather than use the spatial baseline | Bayesian spatial model · Semi-synthetic, homogeneous reporting | AUC: 0.558 -> 0.577; 0.019 | Helped |
| Use heterogeneous rather than homogeneous reporting rates | Bayesian spatial model · Hurricane Ida, NYC future reports | AUC: 0.682 -> 0.680; -0.002 | No clear effect |
| Use heterogeneous rather than homogeneous reporting rates | Bayesian spatial model · Hurricane Ida, NYC future reports | RMSE: 0.360 -> 0.355; -0.004 | Helped |
| Use heterogeneous reporting rather than the GP baseline | Bayesian spatial model · Hurricane Ida, NYC future reports | AUC: 0.629 -> 0.680; 0.051 | Helped |
| Use heterogeneous reporting rather than the spatial baseline | Bayesian spatial model · Hurricane Ida, NYC future reports | AUC: 0.647 -> 0.680; 0.033 | Helped |
| Use heterogeneous reporting rather than the GP baseline | Bayesian spatial model · Hurricane Ida, NYC future reports | RMSE: 0.417 -> 0.355; -0.062 | Helped |
| Use heterogeneous reporting rather than the spatial baseline | Bayesian spatial model · Hurricane Ida, NYC future reports | RMSE: 0.395 -> 0.355; -0.040 | Helped |
Surprising findings
- The homogeneous-reporting model achieves essentially the same predictive AUC as the heterogeneous model on real Ida data (0.682 vs 0.680), yet the heterogeneous model yields more equitable inspection allocations.
- Univariate models found negative coefficients for population density, which the authors note may be counter to intuition and reflects a limitation of the uniform node prior.
Limitations
- Assumes no false-positive reports and a uniform prior on event occurrence across nodes, which may not hold (e.g., lower-lying or larger tracts).
- Uses binarized report data, ignoring report counts (96.5% of locations have zero or one report).
- Relies on Ising spatial correlation assumption without explicitly modeling shared infrastructure or weather; identifiability may be a challenge for alternatives.
Experimental setup
Datasets: NYC 311 street flood reports (Hurricane Ida, Henri, Tropical Storm Ophelia) 2020 Decennial Census demographic features
Benchmarks: NYC 311 Hurricane Ida future reports (held-out test period) Semi-synthetic simulation with known latent states
Metrics: AUC RMSE equity of inspection allocation (population share served)
Baselines: Homogeneous reporting model Spatial baseline (neighbor report fraction) Gaussian Process baseline
Builds on: Ising model Single-Variable Exchange Algorithm Swendsen-Wang algorithm PU learning
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