Spatio-temporal Hawkes point processes: statistical inference and simulation strategies

TL;DR

This paper introduces unified simulation and inference methods for spatio-temporal Hawkes point processes, addressing the lack of a common formalism and enhancing modeling capabilities for complex self-exciting phenomena.

Contribution

It develops two simulation techniques and three inference methods, providing a unified framework and practical evaluation for modeling spatio-temporal Hawkes processes.

Findings

Implemented effective simulation strategies.

Provided self-consistent inference techniques.

Evaluated methods' practical performance.

Abstract

Spatio-temporal Hawkes point processes are a particularly interesting class of stochastic point processes for modeling self-exciting behavior, in which the occurrence of one event increases the probability of other events occurring. These processes are able to handle complex interrelationships between stochastic and deterministic components of spatio-temporal phenomena. However, despite its widespread use in practice, there is no common and unified formalism and every paper proposes different views of these stochastic mechanisms. With this in mind, we implement two simulation techniques and three unified, self-consistent inference techniques, which are widely used in the practical modeling of spatio-temporal Hawkes processes. Furthermore, we provide an evaluation of the practical performance of these methods, while providing useful code for reproducibility.