“Stationary” point processes are uncommon on 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.

Second-order and local characteristics of network intensity functions

The last decade has witnessed an increase of interest in the spatial analysis of structured point patterns over networks whose analysis is challenging because of geometrical complexities and unique methodological problems. In this context, it is essential to incorporate the network specificity into the analysis as the locations of events are restricted to areas covered by line segments. Relying on concepts originating from graph theory, we extend the notions of first-order network intensity functions to second-order and local network intensity functions. We consider two types of local indicators of network association functions which can be understood as adaptations of the primary ideas of local analysis on the plane. We develop the nodewise and cross-hierarchical type of local functions. A real data set on urban disturbances is also presented.

SpNetPrep: An R package using Shiny to facilitate spatial statistics on road networks

Spatial statistics is an important field of data science with many applications in very different areas of study such as epidemiology, criminology, seismology, astronomy and econometrics, among others. In particular, spatial statistics has frequently been used to analyze traffic accidents datasets with explanatory and preventive objectives. Traditionally, these studies have employed spatial statistics techniques at some level of areal aggregation, usually related to administrative units. However, last decade has brought an increasing number of works on the spatial incidence and distribution of traffic accidents at the road level by means of the spatial structure known as a linear network. This change seems positive because it could provide deeper and more accurate investigations than previous studies that were based on areal spatial units. The interest in working at the road level renders some technical difficulties due to the high complexity of these structures, specially in terms of manipulation and rectification. The R Shiny app SpNetPrep, which is available online and via an R package named the same way, has the goal of providing certain functionalities that could be useful for a user which is interested in performing an spatial analysis over a road network structure.

Nearest-neighbour Markov point processes on graphs with Euclidean edges

We define nearest-neighbour point processes on graphs with Euclidean edges and linear networks. They can be seen as analogues of renewal processes on the real line. We show that the Delaunay neighbourhood relation on a tree satisfies the Baddeley‒Møller consistency conditions and provide a characterisation of Markov functions with respect to this relation. We show that a modified relation defined in terms of the local geometry of the graph satisfies the consistency conditions for all graphs with Euclidean edges that do not contain triangles.