On the trend detection of time-ordered intensity images of point processes on linear networks

Spatial point processes on linear networks are increasingly getting attention in different disciplines such as traffic accidents and street crime analysis. Dealing with a set of time-ordered point patterns on a linear network over a period, helps in obtaining a time series of estimated intensity images. In this article, we combine the problem of estimating the intensity and relative risk of point patterns on linear networks with trend detection in time-ordered observations. Taking the temporal autocorrelation between consecutive time-ordered intensity and relative risk images into account, we make use of the Mann–Kendall trend test to look for potential locations in the network where the estimated intensity and/or relative risk show evidence of a monotonic trend. The monthly time-ordered spatial point patterns of fatal traffic accidents and street crimes in the city of London, UK, in the period of January 2013 to December 2017, are used as an application.