Journal Article

stelfi: An R package for fitting Hawkes and log‐Gaussian Cox point process models

Helsdingen, Alec B. M., Jones‐Todd, Charlotte M.

2024

Overview

Modelling spatial and temporal patterns in ecology is imperative to understand the complex processes inherent in ecological phenomena. Log‐Gaussian Cox processes are a popular choice among ecologists to describe the spatiotemporal distribution of point‐referenced data. In addition, point pattern models where events instigate others nearby (i.e., self‐exciting behaviour) are becoming increasingly popular to infer the contagious nature of events (e.g., animal sightings). While there are existing R packages that facilitate fitting spatiotemporal point processes and, separately, self‐exciting models, none incorporate both. We present an R package, stelfi, that fits spatiotemporal self‐exciting and log‐Gaussian Cox process models using Template Model Builder through a range of custom‐written C++ templates. We illustrate the use of stelfi's functions fitting models to Sasquatch (bigfoot) sightings data within the USA. The structure of these data is typical of many seen in ecology studies. We show, from a temporal Hawkes process to a spatiotemporal self‐exciting model, how the models offered by the package enable additional insights into the temporal and spatial progression of point pattern data. We present extensions to these well‐known models that include spatiotemporal self‐excitation and joint likelihood models, which are better suited to capture the complex mechanisms inherent in many ecological data. The package stelfi offers user‐friendly functionality, is open source, and is available from CRAN. It offers the implementation of complex spatiotemporal point process models in R for applications even beyond the field of ecology. We introduce the R package stelfi, available from the Comprehensive R Archive Network. This package allows users to fit temporal self‐exciting Hawkes models, spatial and spatiotemporal log‐Gaussian Cox process models and self‐exciting spatiotemporal models. The functionality of stelfi is illustrated using Sasquatch (bigfoot) sightings data shipped with the package.

• Publisher: John Wiley & Sons, Inc,John Wiley and Sons Inc,Wiley
• Subject: Approximation / Ecologists / Ecology / Gaussian process / Hawkes process / log‐Gaussian Cox process / Maximum likelihood method / Partial differential equations / point‐referenced data / Random variables / Self excitation / self‐exciting / Spatial distribution / Spatial Ecology / spatiotemporal / Template Model Builder / Temporal distribution