A Spatiotemporal Gamma Shot Noise Cox Process

TL;DR

This paper introduces a novel spatiotemporal shot noise Cox process driven by gamma random measures, offering a flexible yet tractable model for complex spatial-temporal data with an efficient Bayesian inference method.

Contribution

It proposes a new discrete-time Cox process with gamma-driven intensity, deriving key properties and developing a Bayesian inference approach with advanced MCMC techniques.

Findings

Model captures persistence and global trends.

Efficient inference via Markov Chain Monte Carlo.

Application successfully models wildfire data.

Abstract

A new discrete-time shot noise Cox process for spatiotemporal data is proposed. The random intensity is driven by a dependent sequence of latent gamma random measures. Some properties of the latent process are derived, such as an autoregressive representation and the Laplace functional. Moreover, these results are used to derive the moment, predictive, and pair correlation measures of the proposed shot noise Cox process. The model is flexible but still tractable and allows for capturing persistence, global trends, and latent spatial and temporal factors. A Bayesian inference approach is adopted, and an efficient Markov Chain Monte Carlo procedure based on conditional Sequential Monte Carlo is proposed. An application to georeferenced wildfire data illustrates the properties of the model and inference.