Construct · 2 names · 2 citations

Where does self-exciting point process collide?

Different names. Different fields. One construct. One map.

● jangle · one construct, many names Nearest construct by meaning·not indexed
the same self-exciting intensity, renamed ETAS for earthquakesself-excitingpoint process2 NAMESHawkes processHAWKES · SELF-EXCITINGETAS modelOGATA · ETAS

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1971Hawkes process1988ETAS model
2026

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Statistics / probability

Each event raises the chance of the next

A self-exciting point process is a model for events in time whose instantaneous rate (conditional intensity) jumps up after each event and then decays, so that past events raise the probability of future ones and activity arrives in clusters rather than independently. Hawkes's 1971 Spectra of some self-exciting and mutually exciting point processes gave the construct its enduring mathematical form, and in statistics it is usually called the Hawkes process. The referent is a stochastic process defined by a baseline rate plus a triggering kernel, fitted to any clustered event stream.[1]

Unit
The conditional intensity: a baseline rate plus the summed influence of past events
Recovery means
Not applicable
Measured by
Specified by the baseline rate and triggering kernel and fitted by maximum likelihood to event times

Seismology

Every quake can trigger its own aftershocks

Seismologists use exactly the same construct under a different name: the epidemic-type aftershock sequence (ETAS) model treats every earthquake, of any size, as capable of triggering its own aftershocks, so the seismicity rate is a background rate plus the decaying influence of all past events. Ogata's 1988 Statistical models for earthquake occurrences and residual analysis for point processes built ETAS as a self-exciting point process with an Omori-type triggering kernel. It is not a different model from the statistician's Hawkes process but the same latent thing wearing a seismological name, a jangle in which one construct travels as 'Hawkes process' in one literature and 'ETAS' in another.[2]

Unit
The seismicity rate: a background rate plus Omori-decaying triggering from past quakes
Recovery means
Not applicable
Measured by
Fitted by maximum likelihood to an earthquake catalogue, estimating background rate, productivity, and Omori decay parameters

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Nearby collisions

aftershock2 fields · 2 citationsinvariant · one construct, two systemsbaseline2 fields · 2 citationsjingle · one word, two constructsconditional3 fields · 3 citationsjingle · one word, three constructs

References

  1. Hawkes, A. G. (1971). Spectra of some self-exciting and mutually exciting point processes. Biometrika, 58(1), 83–90. https://doi.org/10.1093/biomet/58.1.83
  2. Ogata, Y. (1988). Statistical models for earthquake occurrences and residual analysis for point processes. Journal of the American Statistical Association, 83(401), 9–27. https://doi.org/10.1080/01621459.1988.10478560

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