Point Processes on Directed Linear Networks

Self-exciting point process modelling of crimes on linear networks

Although there are recent developments for the analysis of first and second-order characteristics of point processes on networks, there are very few attempts in introducing models for network data. Motivated by the analysis of crime data in Bucaramanga (Colombia), we propose a spatiotemporal Hawkes point process model adapted to events living on linear networks. We first consider a non-parametric modelling strategy, for which we follow a non-parametric estimation of both the background and the triggering components. Then we consider a semi-parametric version, including a parametric estimation of the background based on covariates, and a non-parametric one of the triggering effects. Our model can be easily adapted to multi-type processes. Our network model outperforms a planar version, improving the fitting of the self-exciting point process model.

Analysis of Water Deer Roadkills Using Point Process Modeling in Chungcheongnamdo, South Korea

The expansion of road networks and increased traffic loads have resulted in an increase in the problem of wildlife roadkill, which has a serious impact on both human safety and the wildlife population. However, roadkill data are collected primarily from the incidental sighting, thus they often lack the true-absence information. This study aims to identify the factors associated with Korean water deer (Hydropotes inermis) roadkill in Korea using the point processing modeling (PPM) approach. Water deer roadkill point data were fitted with explanatory variables derived from forest cover type, topography, and human demography maps and an animal distribution survey. Water deer roadkill showed positive associations with road density, human population density, road width, and water deer detection point density. Slope and elevation showed negative associations with roadkill. The traffic volume and adjacent water deer population may be the major driving factors in roadkill events. The results also imply that the PPM can be a flexible tool for developing roadkill mitigation strategy, providing analytical advantages of roadkill data, such as clarification of model specification and interpretation, while avoiding issues derived from a lack of true-absence information.