Open Access
August 2018 A Review of Self-Exciting Spatio-Temporal Point Processes and Their Applications
Alex Reinhart
Statist. Sci. 33(3): 299-318 (August 2018). DOI: 10.1214/17-STS629


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.


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Alex Reinhart. "A Review of Self-Exciting Spatio-Temporal Point Processes and Their Applications." Statist. Sci. 33 (3) 299 - 318, August 2018.


Published: August 2018
First available in Project Euclid: 13 August 2018

zbMATH: 06991118
MathSciNet: MR3843374
Digital Object Identifier: 10.1214/17-STS629

Keywords: Conditional intensity , epidemic-type aftershock sequence , Hawkes process , stochastic declustering

Rights: Copyright © 2018 Institute of Mathematical Statistics

Vol.33 • No. 3 • August 2018
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