Stochastic smoothing of point processes for wildlife-vehicle collisions on road networks

M. I. Borrajo,J. Mateu,C. Comas,S. Costafreda-Aumedes

doi:10.1007/s00477-021-02072-3

Abstract

Wildlife-vehicle collisions on road networks represent a natural problem between human populations and the environment, that affects wildlife management and raise a risk to the life and safety of car drivers. We propose a statistically principled method for kernel smoothing of point pattern data on a linear network when the first-order intensity depends on covariates. In particular, we present a consistent kernel estimator for the first-order intensity function that uses a convenient relationship between the intensity and the density of events location over the network, which also exploits the theoretical relationship between the original point process on the network and its transformed process through the covariate. We derive the asymptotic bias and variance of the estimator, and adapt some data-driven bandwidth selectors to estimate the optimal bandwidth. The performance of the estimator is analysed through a simulation study under inhomogeneous scenarios. We present a real data analysis on wildlife-vehicle collisions in a region of North-East of Spain.

Highlights

Spatial point processes are mathematical models that describe the geometrical structure of patterns formed by events, which are distributed randomly in number and space
We propose a statistically principled method for kernel smoothing of point pattern data on a linear network when the first-order intensity depends on covariates
We present a consistent kernel estimator for the first-order intensity function that uses a convenient relationship between the intensity and the density of events location over the network, which exploits the theoretical relationship between the original point process on the network and its transformed process through the covariate

Summary

Introduction

Spatial point processes are mathematical models that describe the geometrical structure of patterns formed by events, which are distributed randomly in number and space. Rakshit et al (2019) proposed a fast kernel intensity estimator based on a two-dimensional convolution which can be computed rapidly even on large networks None of these approaches take into account covariate information that is expected to have a direct effect on the intensity function. The classical kernel estimation approach is often unsuitable in such cases and echoing (Barr and Schoenberg 2010), we argue that kernel-based approaches may be unsatisfactory if they miss out covariate information In this line, Borrajo et al (2020) consider kernel estimation of the intensity under the presence of spatial covariates when the point pattern lives in the Euclidean plane. In this paper we tackle this problem and propose a covariate-based kernel estimation for point processes on linear networks, showing its advantages on a wildlife-vehicle collision problem.

Wildlife-vehicle collisions on road networks

Point processes on linear networks

Covariate-dependent kernel-based intensity estimation

A note on covariates on networks

Bootstrap bandwidth

Bandwidth selection methods

Rule-of-thumb

Simulation study

Simulated examples

Case study: wildlife-vehicle collisions on a road network

Findings

Discussion