A spatio-temporal multi-scale model for Geyer saturation point process: application to forest fire occurrences

TL;DR

This paper introduces a novel spatio-temporal multi-scale Geyer saturation point process model, enabling better analysis of phenomena like forest fires that depend on multiple spatial and temporal scales.

Contribution

It extends classical Gibbs models to a multi-scale framework and demonstrates its application to forest fire data, including inference methods and simulation techniques.

Findings

The model captures multi-scale dependencies in forest fire data.

Simulation and inference methods are tailored for the new model.

Application to real forest fire data in Southern France.

Abstract

Because most natural phenomena exhibit dependence at multiple scales like locations of earthquakes or forest fire occurrences, spatio-temporal single-scale point process models are unrealistic in many applications. This motivates us to construct generalizations of classical Gibbs models. In this paper, we extend the Geyer saturation point process model to the spatio-temporal multi-scale framework. The simulation process is carried out through a birth-death Metropolis-Hastings algorithm. In a simulation study, we compare two common methods for statistical inference in Gibbs models: the pseudo-likelihood and logistic likelihood approaches that we tailor to this model. Finally, we illustrate this new model on forest fire occurrences modeling in Southern France.