This review of self-exciting spatio-temporal point processes and their applications explains the basic theory, surveys related estimation and inference techniques from each field, highlights several key applications, and suggests directions for future research.
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. (publisher abstract modified)
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