A Review of Self-Exciting Spatio-Temporal Point Processes and Their Applications

TL;DR

This review comprehensively covers the theory, estimation methods, applications, and future directions of self-exciting spatio-temporal point process models used in various fields like seismology, epidemiology, and criminology.

Contribution

It provides a thorough survey of the foundational theory, recent methodological advances, and key applications of self-exciting spatio-temporal point processes.

Findings

Summarizes estimation and inference techniques across fields

Highlights applications in earthquake, disease, and crime modeling

Suggests future research directions in the field

Abstract

Self-exciting spatio-temporal point process models predict the rate of events as a function of space, time, and the previous history of events. These models naturally capture triggering and clustering behavior, and have been widely used in fields where spatio-temporal clustering of events is observed, such as earthquake modeling, infectious disease, and crime. In the past several decades, advances have been made in estimation, inference, simulation, and diagnostic tools for self-exciting point process models. In this review, I describe the basic theory, survey related estimation and inference techniques from each field, highlight several key applications, and suggest directions for future research.