The search-threshold test

Published July 2026 · Data window: MPD stops 2023–2025, searches with recorded outcomes

The question: Does it take less suspicion to get searched if you are Black?

The answer: Yes. The inferred bar sits at about 0.05 for Black people vs 0.08 for everyone else: searches of Black people proceed on thinner suspicion.

Equal hit rates can hide discrimination: if officers search one group on thinner suspicion, more low-evidence searches happen but the hit rate alone cannot show it (the infra-marginality problem). The threshold model infers the evidence bar itself. The model finds that searches of Black people proceed on a LOWER inferred evidence bar: a threshold of 0.05 vs 0.08 for everyone else (gap 0.038, 95% interval 0.019 to 0.059, posterior probability 100% that the Black threshold is lower). This is the disparity that equal hit rates are structurally unable to reveal.

0.05 vs 0.08

Inferred search thresholds, Black vs everyone else (citywide, stop-weighted): the assessed probability of finding contraband above which a search happens under the model. Lower = searched on thinner suspicion. Gap +0.038 (95% interval 0.02 to 0.06).

District	Black threshold	95% interval	Non-Black threshold	95% interval	Searches (N)
District 1	0.03	0.02 to 0.04	0.06	0.05 to 0.08	2,026
District 2	0.04	0.03 to 0.06	0.08	0.06 to 0.09	768
District 3	0.06	0.04 to 0.08	0.11	0.09 to 0.13	1,472
District 4	0.03	0.02 to 0.04	0.06	0.04 to 0.07	1,271
District 5	0.06	0.04 to 0.08	0.12	0.10 to 0.14	2,153
District 6	0.04	0.03 to 0.06	0.08	0.06 to 0.10	3,234
District 7	0.04	0.03 to 0.06	0.08	0.06 to 0.10	3,435

Districts in numeric order; this is not a ranking. Absolute threshold levels are weakly identified in this model family; the RACE GAP within and across districts is the identified quantity, which is why the finding above is stated in terms of the gap.

How this number is built (and where it's soft)

Design (Simoiu, Corbett-Davies & Goel 2017). For each district and race group, stops carry a latent signal of contraband; a search happens when the signal clears that cell's threshold. Signal distributions (Beta family with race and district structure) and thresholds are inferred jointly from stops, searches, and hits per cell; the hierarchy across districts is what identifies the model.
What counts as a search. Consent, warrant, and protective pat-down searches with a recorded seizure outcome (0 searches with no recorded outcome are excluded and counted; the source has no outcome field for probable-cause searches, 4,342 of which are likewise excluded and counted).
Fit quality is checked, not assumed. Every cell's observed search and hit counts must fall inside the model's central 95% posterior predictive interval (which accounts for each cell's own sampling noise); in this fit, 0 of 14 cells fall outside on searches and 0 on hits. Largest posterior-mean deviation: 0.1 points on search rates, 5.4 on hit rates. A direction is asserted only when the check passes AND the gap's 95% posterior interval excludes zero.
Model-based, and says so. Conclusions are conditional on the Beta-signal family and the hierarchy; this is the standard remedy for infra-marginality, not a model-free fact. The hit-rate comparison on the searches page stays alongside as the model-free view.
Computation. Fit offline by MCMC (emcee affine-invariant ensemble (DE moves), 32,280 posterior samples, mean acceptance 0.19, convergence criterion met: post-burn chain at least 50 autocorrelation times long); this page renders the stored posterior, model version beta-signal-hier-v2, stop batch 4.
Exclusions (reported, not dropped quietly). Unknown-race (15,373) and unmapped-district (3,057) persons are excluded and counted, as on every page.