Self-exciting point processes

Alex Reinhart – Updated November 15, 2017 notebooks · refsmmat.com

See also spatiotemporal point processes.

I’ve written a full review of this topic; see Reinhart, A. (2018). A review of self-exciting spatio-temporal point processes and their applications. Statistical Science. https://arxiv.org/abs/1708.02647

Properties

ETAS

The basic approach comes from Epidemic-Type Aftershock Models, where earthquakes are caused by some constant background process and then induce further aftershocks when they arrive. There’s a whole series of papers by Ogata; some highlights from the field:

Epidemic/endemic models

The ETAS has been adapted to epidemiology (see also epidemic models):

Stochastic declustering

A self-exciting point process can be interpreted as a Poisson cluster process, as mentioned above. It could be interesting to decluster it, meaning to remove the events which were “excited” by another, and leave only the background events which occurred spontaneously. (In the earthquake literature, this means removing the aftershocks and keeping only the main shocks.) Stochastic declustering is this procedure.

Multivariate processes

Evaluation

How do we evaluate predictions made by a self-exciting point process model?