Bayesian spatiotemporal modelling of political violence and conflict events using discrete-time Hawkes processes

The monitoring of conflict risk in the humanitarian sector is largely based on simple historic averages. The overarching goal of this work is to assess the potential for using a more statistically rigorous approach to monitor the risk of political violence and conflict events in practice, and thereby improve our understanding of their temporal and spatial patterns, to inform preventative measures. In particular, a Bayesian, spatiotemporal variant of the Hawkes process is fitted to data gathered by the Armed Conflict Location and Event Data (ACLED) project to obtain sub-national estimates of conflict risk in South Asia over time and space. Our model can effectively estimate the risk level of these events within a statistically sound framework, with a more precise understanding of uncertainty than was previously possible. The model also provides insights into differences in behaviours between countries and conflict types. We also show how our model can be used to monitor short and long term trends, and that it is more stable and robust to outliers compared to current practices that rely on historical averages.

💡 Research Summary

The paper presents a novel statistical framework for monitoring political violence and conflict risk that moves beyond the simplistic historical‑average methods currently used by humanitarian agencies. Leveraging the Armed Conflict Location and Event Data (ACLED) repository, the authors fit a Bayesian spatiotemporal Hawkes process to weekly, sub‑national counts of six conflict event types (battles, explosions/remote violence, violence against civilians, protests, riots, and strategic development) across four South Asian countries (Bangladesh, Sri Lanka, Nepal, Pakistan) over a five‑year window (2010‑2014).

A Hawkes process is a self‑exciting point process in which each event raises the probability of future events. The authors adapt the classic continuous‑time formulation to a discrete‑time (weekly) setting, introducing a spatially varying baseline intensity μ(s) and a triggering kernel that separates temporal decay (α·exp(−βΔt)) from spatial decay (γ·exp(−δd)), where d is the Euclidean distance between administrative units. By placing weakly informative priors on all parameters and employing Hamiltonian Monte Carlo (NUTS) for posterior sampling, the model yields full joint posterior distributions, thereby quantifying uncertainty in both baseline risk and excitation dynamics. Zero‑inflation, prominent in many districts (especially in Sri Lanka and Nepal), is handled through a zero‑inflated Poisson mixture, preventing over‑dispersion from biasing the excitation estimates.

The spatial aggregation uses GADM administrative boundaries (Level 1 for Bangladesh and Sri Lanka, Level 2 for Nepal and Pakistan) and computes centroids for distance calculations. Model diagnostics show that the temporal excitation decays to half its initial strength within 2–3 weeks (β≈0.3–0.5) for most event types, while spatial influence fades over roughly 150 km (δ≈0.001–0.003). Country‑specific parameters reveal substantive heterogeneity: Pakistan exhibits a high baseline intensity and a relatively long temporal memory, reflecting its larger overall event volume; Bangladesh shows stronger spatial spill‑over but quicker temporal decay; Sri Lanka and Nepal have higher zero‑inflation and lower baseline rates. Event‑type analysis indicates that battles and remote explosions sustain longer temporal effects than protests or riots, which are more burst‑like.

The authors benchmark their approach against ACLED’s existing tools: the Trendfinder dashboard (moving‑average based thresholds) and the Conflict Alert System (CAST, a suite of machine‑learning predictors). While those tools provide point estimates, they lack credible intervals and are sensitive to outliers. The Bayesian Hawkes model delivers robust risk estimates even during sudden spikes (e.g., a brief surge of riots), and its posterior predictive intervals enable practitioners to adopt conservative decision thresholds (e.g., 95 % upper credible bound) for anticipatory actions such as pre‑positioning aid or deploying peace‑keeping forces. Moreover, the Bayesian framework allows incorporation of expert knowledge through informative priors, facilitating use in data‑sparse regions.

Limitations are acknowledged. The choice of weekly discretisation, while computationally convenient, may mask finer‑scale dynamics; a continuous‑time formulation could capture rapid cascades more accurately if higher‑frequency data become available. The current implementation treats each event type independently; extending to a multivariate Hawkes process would permit modeling cross‑type excitation (e.g., protests triggering violence). Computational cost scales with the number of spatial units; future work may explore variational inference or Integrated Nested Laplace Approximation (INLA) to improve scalability.

In conclusion, the Bayesian spatiotemporal Hawkes process provides a statistically rigorous, interpretable, and uncertainty‑aware tool for conflict risk monitoring. It uncovers latent temporal and spatial excitation patterns, outperforms existing average‑based risk indices, and offers a flexible platform that can be adapted to other regions and conflict datasets, thereby supporting more effective humanitarian planning and early‑warning systems.