Bias from positional averaging in interaction-range estimation

Determine whether positional averaging of social groups into centroid-based macro-pedestrians systematically overcorrects the estimated interaction range of the modified Diggle–Gates–Stibbard spatial point-process model for waiting pedestrians.

Background

The paper models waiting pedestrians using a Gibbs spatial point process with an inhomogeneous intensity function and a modified Diggle–Gates–Stibbard interaction function. To account for social groups, the authors detect groups from pairwise distances and contact durations, replace each detected group by a macro-pedestrian located at the group centroid, and refit the model to the resulting aggregated configurations.

The authors observe that aggregation removes within-group distances and measures distances between groups and neighboring pedestrians from group centroids rather than from the nearest group members. These geometric changes can make the aggregated patterns appear more regular and may lead the estimation procedure to infer interaction ranges that are too large. The paper therefore leaves unresolved whether positional averaging systematically overcorrects the interaction range, especially because the ungrouped estimation procedure was previously found to underestimate repulsion.