Index: Reinhart 2018 - Self-Exciting Spatio-Temporal Point Processes

Reinhart 2018 - Self-Exciting Spatio-Temporal Point Processes

Routing Summary

Full capture of Reinhart (2018), A Review of Self-Exciting Spatio-Temporal Point Processes and Their Applications (Stat. Sci., arXiv:1708.02647): Hawkes/ETAS conditional intensity, likelihood and EM, declustering, simulation, inference, diagnostics, and applications.

• Need the paper on one page or the section map? → Reinhart 2018 - Self-Exciting Spatio-Temporal Point Processes - Overview
• Need definitions of conditional intensity, Hawkes, branching ratio, marks? → Reinhart 2018 - Hawkes Processes and Conditional Intensity
• Need the likelihood, compensator, EM algorithm, Bayesian sampling? → Reinhart 2018 - Likelihood, EM and Bayesian Estimation
• Need ZOV declustering, FLP, MISD? → Reinhart 2018 - Stochastic Declustering
• Need simulation, bootstrap, residual diagnostics? → Reinhart 2018 - Simulation, Inference and Diagnostics
• Need ETAS / Omori-Utsu / Gutenberg-Richter and a PyMC sketch (E65)? → Reinhart 2018 - ETAS Earthquake Models and Omori Law
• Need crime, epidemic, network applications and the caveat? → Reinhart 2018 - Crime, Epidemic and Network Applications

Concept Map

Concept	Note	Type	Depends On	Key Result
Conditional intensity, Hawkes, cluster representation	Reinhart 2018 - Hawkes Processes and Conditional Intensity	definition	none	$m=\int g<1$ gives cluster size $1/(1-m)$
Likelihood, EM, Bayesian	Reinhart 2018 - Likelihood, EM and Bayesian Estimation	theorem	Hawkes	$\ell =\sum \log \lambda -\iint \lambda$; $\mathrm{Pr}(u_i=j)=g_{ij}/{\lambda }_i$
Declustering	Reinhart 2018 - Stochastic Declustering	theorem	EM	$\hat{\mu }=\frac{1}{T}\sum \mathrm{Pr}(u_i=0)k(s-s_i)$
Simulation, inference, diagnostics	Reinhart 2018 - Simulation, Inference and Diagnostics	theorem	declustering	cluster simulation; bootstrap; Voronoi residuals
ETAS / Omori	Reinhart 2018 - ETAS Earthquake Models and Omori Law	example	Hawkes, EM	$m=\frac{K_0{c}^{1-p}}{p-1}\frac{\beta }{\beta -\alpha }$
Crime, epidemic, networks	Reinhart 2018 - Crime, Epidemic and Network Applications	example	ETAS	background/triggered split needs care

Notes

• Reinhart 2018 - Self-Exciting Spatio-Temporal Point Processes - Overview — CONTAINS: question, contributions, motivating PyMC examples (E65, E07), Source Map.
• Reinhart 2018 - Hawkes Processes and Conditional Intensity — CONTAINS: conditional intensity, Hawkes, cluster theorem, marks, Figs. 1-2, Python simulation.
• Reinhart 2018 - Likelihood, EM and Bayesian Estimation — CONTAINS: Janossy derivation, compensator approximations, EM, boundary bias, Ross partition, O(n) recursion code, PyMC sketch.
• Reinhart 2018 - Stochastic Declustering — CONTAINS: ZOV Alg. 1-2, FLP Alg. 3, MISD, Python.
• Reinhart 2018 - Simulation, Inference and Diagnostics — CONTAINS: Alg. 4-6, asymptotics, partial likelihood, thinning/super-thinning, Voronoi residuals.
• Reinhart 2018 - ETAS Earthquake Models and Omori Law — CONTAINS: temporal ETAS, branching ratio derivation, findings, E65 PyMC sketch.
• Reinhart 2018 - Crime, Epidemic and Network Applications — CONTAINS: Mohler, Meyer, Schoenberg, Fox, Zipkin, Green models; conclusion.

Sources

Reinhart 2018 - Self-Exciting Spatio-Temporal Point Processes Review (arXiv:1708.02647v2).

See Also

Simpson 2016 - Going Off Grid - Overview | Social Network Models | Survival Analysis