Inhomogeneous spatio-temporal point processes on linear networks for visitors’ stops data
Nicoletta D’Angelo, Giada Adelfio, Antonino Abbruzzo, Jorge Mateu
The Annals of Applied Statistics · 2022 · Volume 16 · Issue 2
Abstract
We analyse the spatio-temporal distribution of visitors’ stops by touristic attractions in Palermo (Italy), using theory of stochastic point processes living on linear networks. We first propose an inhomogeneous Poisson point process model with a separable parametric spatio-temporal first-order intensity. We account for the spatial interaction among points on the given network, fitting a Gibbs point process model with mixed effects for the purely spatial component. This allows us to study first-order and second-order properties of the point pattern, accounting both for the spatio-temporal clustering and interaction and for the spatio-temporal scale at which they operate. Due to the strong degree of clustering in the data, we then formulate a more complex model, fitting a spatio-temporal log-Gaussian Cox process to the point process on the linear network, addressing the problem of the choice of the most appropriate distance metric.
Keywords
Gibbs point processes, Global Positioning System, intensity estimation, linear networks, log-Gaussian Cox processes, spatio-temporal point processes
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