A Review of Self-Exciting Spatio-Temporal Point Processes and Their Applications
arXiv:1708.02647 · doi:10.1214/17-STS629
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.
30 pages, 3 figures
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- Asymmetric excitation of left- and right-tail extreme events probed using a Hawkes model: application to financial returns
- Graph-based mutually exciting point processes for modelling event times in docked bike-sharing systems
- A Multidimensional Fractional Hawkes Process for Multiple Earthquake Mainshock Aftershock Sequences
- Mitigating Performance Saturation in Neural Marked Point Processes: Architectures and Loss Functions