A Surrogate-Mark Framework for Modeling Hawkes Processes Under Spatial Uncertainty

Music City Center 

Hawkes processes are commonly used to capture clustered structures in point pattern data, as they allow each event to elevate the chance of subsequent event occurrences. However, this triggering mechanism is difficult to model accurately when spatial information is measured at varying levels of precision. A common strategy is to use only events with the most precise geolocation, but this can lead to both a loss of information and inaccurate estimates of the underlying triggering structure. In this research, we propose a novel framework that retains events with less precise location data by incorporating location-relevant marks as surrogate measures of spatial information. We integrate this surrogate into nonparametric intensity estimation through a modified weighting scheme in the Model-Independent Stochastic Declustering algorithm. Simulation studies verify that the proposed method can recover the triggering structure more accurately than standard approaches. We further illustrate its usefulness with an application to real-world data, demonstrating how the suggested framework can enhance our understanding of space-time clustering by carefully incorporating imprecise events.

Spatio-temporal point process

Geolocation error

Two-phase analysis

Terrorism data

Hawkes process 

Korean International Statistical Society