Chicago homicide hotspots split evenly between persistent risk and contagion

Homicide hotspots in Chicago are not produced by a single mechanism. A new study applying a Bayesian Cox–Hawkes point process model to 2,087 homicides recorded in the city between 1 January 2018 and 31 December 2021 finds that the estimated intensity of lethal violence divides approximately equally between a persistent background risk and a self-exciting component, in which each homicide raises the short-term probability of further killings nearby. The work, published open access in Crime Science, argues that prevention strategies built exclusively on near-repeat or retaliatory dynamics risk misalignment in places where violence instead reflects enduring risk.

The study, conducted by Diego J. Maldonado-Guzmán, addresses a long-standing ambiguity in criminology. Crime tends to concentrate at particular times and places, but two competing accounts explain why. The risk heterogeneity perspective, sometimes called the “flag” account, holds that certain areas carry enduring characteristics—structural disadvantage, discriminatory housing policies, residential instability, land-use patterns such as nightlife concentrations and vacation rentals—that make them inherently higher-risk locations. Under this view, observed clustering is spurious: offences pile up in risky places, but one event does not cause the next. The event dependence perspective, or “boost” account, instead proposes a causal chain, in which one crime—such as a gang attack triggering retaliation—genuinely increases the short-term risk of subsequent offences nearby.

Distinguishing these mechanisms matters because police responses are built on them. Arrest-focused strategies, rapid property damage mitigation and short-term access control assume event dependence, operating on the assumption that the same perpetrator or associates return to reoffend. Target hardening and proactive patrols draw on risk heterogeneity, seeking to reduce the features that make a place attractive to different offenders. Previous research suggests effectiveness varies by mechanism and crime type: arrests may reduce shootings but appear less effective for property crimes, while proactive policing has shown limited success against shootings in some contexts. Misidentifying the process behind a hotspot can therefore lead to misplaced enforcement.

The analytical tool was a parametric Cox–Hawkes point process model, implemented with the Bayesian Spatiotemporal Point Process (BSTPP) package in Python. The model decomposes homicide intensity into two components: a log-Gaussian Cox process capturing spatially and temporally stable background risk, and a Hawkes process capturing contagion, whereby past events increase the short-term likelihood of subsequent events nearby. The temporal triggering kernel takes an exponential form and the spatial kernel is Gaussian, centred on each event, so the highest probability of a successor homicide occurs at the same location and declines with distance. Estimation used stochastic variational inference over 3,000 iterations with a learning rate of 0.002, and default priors from the BSTPP package.

Data came from Chicago’s open crime portal. After removing incidents with incorrect geocoding, domestic-related incidents and duplicate cases, the final dataset contained 2,087 homicides from 2018 through 2021. Events from 1 January 2018 to 1 January 2020 trained the model; homicides from 2 January 2020 to 31 December 2021 were reserved for out-of-sample validation. Chicago was chosen partly because its homicide concentration is high: between January 2022 and December 2023, 50% of 1,374 homicides occurred on just 1.2% of all streets, or 26% of streets with at least one homicide.

Descriptive analyses reinforced the case for modelling contagion’s spatial reach. For each homicide, the first three temporal successors were identified, and distances and elapsed times between pairs were calculated across distance bands of 100 to 2,000 metres and temporal windows of 30 to 365 days. In the reported 250–500 metre, 90-day window, intervals between homicides concentrated in the first weeks after the index event: half of the pairs occurred within 44 days and three quarters within 67 days, with a long tail of later successors.

The model’s out-of-sample performance was substantial. The raster log-score averaged −7.69 per validation event against −8.24 for a uniform spatial-risk benchmark, a gain of 0.553 units per event. Average Precision reached 0.5448 against a no-skill baseline of 0.2187, and ROC AUC was 0.814. The Brier score of 0.1387 improved on the uniform benchmark of 0.180. In hotspot terms, the 1% highest-risk cells contained 5.9% of validation homicides, a Predictive Accuracy Index of 5.79; the top 10% of cells captured 39.7% of future homicides, and the top 20% contained about 61%.

The decomposition results were the study’s central finding. Roughly 47.5–50% of homicides were attributed to self-excitation, meaning they occurred because of homicides that took place since the beginning of the observation period, with the remainder assigned to persistent background risk. The reproduction number—each homicide’s expected number of directly triggered events—had a posterior median of 0.58 (90% credible interval 0.53–0.63), indicating a subcritical process in which chains of violence fade rather than escalate indefinitely. This is markedly higher than reproduction numbers of roughly 0.15–0.20 reported for Chicago shootings in earlier work, a difference the author suggests may reflect that completed homicides are more closely tied to retaliatory violence than shootings overall.

Both the spatial and temporal reach of contagion proved limited. The spatial triggering effect was concentrated, on average, between 370 and 544 metres from the prior homicide. Temporally, the triggering effect declined to half its initial magnitude after approximately 103 days (90% credible interval 90.2–118 days), to 10% after about 355 days and to 5% after about 461 days, with most of its strength in the first few months. The estimated background intensity also varied over time, peaking early in 2018, dipping in late 2018 and early 2019, and recovering around mid-2019, though credible intervals indicated considerable uncertainty in these fluctuations.

The author is careful about interpretation. The self-excitation component represents statistical dependence between events, not direct causal transmission, and cannot determine whether any individual homicide was triggered by another. The latent background component captures persistent variation in risk but, because no socioeconomic, land-use, demographic, policing or gang-related covariates were included, it should be read as persistent latent risk rather than evidence of structural causation. Nor does the dataset identify which incidents were gang related; the discussion of gang rivalry and retaliation is theoretically informed rather than empirically verified, although prior research found gang members involved in roughly 50–60% of Chicago homicides. The exponential–Gaussian triggering kernel also imposes a specific functional form that alternative models could relax.

The practical implication is that homicide hotspots cannot be addressed through one prevention logic. Places dominated by persistent background risk are unlikely to respond to situational measures alone, such as increasing patrols near recent homicide scenes, and may require interventions addressing chronic social disadvantage, illicit markets and other place-based conditions. Locations where self-excitation dominates may benefit from rapid responses aimed at interrupting retaliatory cycles. The study also notes that arresting one offender may not halt a retaliatory process operating at group level, and that earlier Chicago research found arresting gang leaders fragmented gangs and increased internal violence. Replication code, supplementary materials and an interactive tool are available to support wider use of the approach.

Subject of Research: Spatiotemporal modelling of homicide hotspots in Chicago separating persistent background risk from self-exciting contagion

Article Title: Homicide hotspots in Chicago: disentangling background persistent risk from contagion dynamics

Article References: Maldonado-Guzmán, D. J. (2026). Homicide hotspots in Chicago: disentangling background persistent risk from contagion dynamics. Crime Science, 15(1), Article 27. https://doi.org/10.1186/s40163-026-00297-7

Image Credits: AI Generated

DOI: 10.1186/s40163-026-00297-7

Keywords: homicide, Chicago, hotspots, Cox–Hawkes process, self-excitation, near-repeat victimization, risk heterogeneity, Bayesian point process, crime prevention, gang violence, spatiotemporal modelling, disentangling