Point Processes

Last update: 21 Apr 2025 21:17
First version: 8 August 2018

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Yet Another Inadequate Placeholder

See also:
• Empirical Process Theory
• Neural Modeling and Data Analysis
• Random Time Changes for Stochastic Processes
• Recurrence Times of Stochastic Processes
• Spatial Patterns in Crime, Especially Clustering/Concentration
• Stochastic Processes
• Time Series

Recommended (big picture):
• Most good general books on stochastic processes cover at least simple point processes; I can particularly recommend Bartlett, Grimmett and Stirzaker, and Kallenberg

Recommended (close-ups):
• David Brillinger
  • "Remarks concerning graphical models for time series and point processes," Revista de Econometria 16 (1996): 1--23
  • "Second-order moments and mutual information in the analysis of time series and point processes," Proceedings of the Conference Statistics 2001 Canada [online]
  • "Nerve Cell Spike Train Data Analysis: A Progression of Technique," Journal of the American Statistical Association 87 (1992): 260--270
• Emery N. Brown, Robert E. Kass and Partha P. Mitra, "Multiple Neural Spike Train Data Analysis: State-of-the-art and Future Challanges", Nature Neuroscience 7 (2004): 456--461 [PDF reprint via Rob]
• Vanessa Didelez, "Graphical models for marked point processes based on local independence", arxiv:0710.5874
• Shinsuke Koyama and Shiegeru Shinomoto, "Empirical Bayes interpretations of random point events", Journal of Physics A: Mathematical and General 38 (2005): L531--L537
• Patrick J. Laub, Thomas Taimre, Philip K. Pollett, "Hawkes Processes", arxiv:1507.02822
• Brad Leun and Philip B. Stark, "Testing Earthquake Predictions", pp. 302--315 in Deborah Nolan and Terry Speed (eds.), Probability and Statistics: Essays in Honor of David A. Freedman (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2008)
• Charles Loeffler, Seth Flaxman, "Is Gun Violence Contagious?", arxiv:1611.06713
• Alex Reinhart, "A Review of Self-Exciting Spatio-Temporal Point Processes and Their Applications", arxiv:1708.02647
• Alex Reinhart and Joel Greenhouse, "Self-exciting point processes with spatial covariates: modeling the dynamics of crime", Journal of the Royal Statistical Society C 67 (2018): 1305--1329, arxiv:1708.03579

To read:
• E. Bacry, K. Dayri, J. F. Muzy, "Non-parametric kernel estimation for symmetric Hawkes processes. Application to high frequency financial data", arxiv:1112.1838
• Emmanuel Bacry, Jean-Francois Muzy, "Second order statistics characterization of Hawkes processes and non-parametric estimation", arxiv:1401.0903
• Adrian Baddeley et al., Spatial Point Patterns: Methodology and Applications with R
• Jérémie Bigot, Sébastien Gadat, Thierry Klein, and Clément Marteau, "Intensity estimation of non-homogeneous Poisson processes from shifted trajectories", Electronic Journal of Statistics 7 (2013): 881--931
• Adrian A. Budini, "Large deviations of ergodic counting processes: a statistical mechanics approach", Physical Review E 84 (2011): 011141, arxiv:1112.2625
• Zhiyi Chi, "Large deviations for template matching between point processes", Annals of Applied Probability 15 (2005): 153--174, math.PR/0503463
• Remy Chicheportiche, Anirban Chakraborti, "A model-free characterization of recurrences in stationary time series", arxiv:1302.3704
• Luca Citi , Demba Ba , Emery N. Brown and Riccardo Barbieri, "Likelihood Methods for Point Processes with Refractoriness", Neural Computation 26 (2014): 237--263
• Jean‐François Coeurjolly Frédéric Lavancier, "Residuals and goodness‐of‐fit tests for stationary marked Gibbs point processes", Journal of the Royal Statistical Society B 75 (2013): 247--276
• Forrest W. Crawford, Daniel Zelterman, "Markov counting models for correlated binary responses", arxiv:1305.1656
• Serguei Dachian, Yury A. Kutoyants
  • "Hypotheses Testing: Poisson Versus Self-exciting", Scandinavian Journal of Statistics 33 (2006): 391, arxiv:0903.4636
  • "On the Goodness-of-Fit Tests for Some Continuous Time Processes", arxiv:0903.4642 ["We present a review of several results concerning the construction of the Cramer-von Mises and Kolmogorov-Smirnov type goodness-of-fit tests for continuous time processes. As the models we take a stochastic differential equation with small noise, ergodic diffusion process, Poisson process and self-exciting point processes"]
• Justin Dauwels, Theophane Weber, Francois Vialatte, Toshimitsu Musha and Andrzej Cichocki, "Quantifying Statistical Interdependence, Part III: N > 2$ Point Processes", Neural Computation 24 (2012): 408--454
• Moritz Deger, Moritz Helias, Stefano Cardanobile, Fatihcan M. Atay, Stefan Rotter, "Non-equilibrium dynamics of stochastic point processes with refractoriness", arxiv:1002.3798
• Peter J. Diggle, Statistical Analysis of Spatial and Spatio-Temporal Point Patterns
• Michael Eichler, Rainer Dahlhaus and Johannes Dueck, "Graphical Modeling for Multivariate Hawkes Processes with Nonparametric Link Functions", Journal of Time Series Analysis 38 (2017): 225--242
• Seth Flaxman, Daniel Neill, Alex Smola, "Correlates of homicide: new space/time interaction tests for spatiotemporal point processes", Heinz College (CMU) Tech Report 409
• Seth Flaxman, Yee Whye Teh, Dino Sejdinovic, "Poisson intensity estimation with reproducing kernels", arxiv:1610.08623
• Yongtao Guan, Abdollah Jalilian, Rasmus Waagepetersen, "Quasi-likelihood for Spatial Point Processes", Journal of the Royal Statistical Society B 77 (2015): 677--697, arxiv:1303.0188
• Eric C. Hall, Rebecca M. Willett, "Tracking Dynamic Point Processes on Networks", IEEE Transactions on Information Theory 62 (2016), arxiv:1409.0031
• Niels Richard Hansen
  • "Penalized maximum likelihood estimation for generalized linear point processes", arxiv:1003.0848
  • "Nonparametric likelihood based estimation of linear filters for point processes", arxiv:1304.0503
• David Harte, "PtProcess: An R Package for Modelling Marked Point Processes Indexed by Time", Journal of Statistical Software 35 (2010): 8
• Matthew T. Harrison, Asohan Amarasingham and Wilson Truccolo, "Spatiotemporal Conditional Inference and Hypothesis Tests for Neural Ensemble Spiking Precision", Neural Computation 27 (2015): 104--150
• Janine Illian, Antti Penttinen, Helga Stoyan, Dietrich Stoyan, Statistical Analysis and Modelling of Spatial Point Patterns
• Sanja Janicevic, Lasse Laurson, Knut Jorgen Maloy, Stephane Santucci, and Mikko J. Alava, "Interevent Correlations from Avalanches Hiding Below the Detection Threshold", Physical Review Letters 117 (2016): 230601
• Alex Kulesza, Ben Taskar, "Determinantal point processes for machine learning", Foundations and Trends in Machine Learning 5 (2012): 123--286, arxiv:1207.6083
• T. Kuna, J. L. Lebowitz and E. R. Speer, "Realizability of point processes", math-ph/0612075
• Gert Nieuwenhuis, "Asymptotic mean stationarity and absolute continuity of point process distributions", Bernoulli 19 (2013): 1612--1636, arxiv:1312.2726
• Christopher J. Paciorek, "Spatial models for point and areal data using Markov random fields on a fine grid", Electronic Journal of Statistics 7 (2013): 946--972
• Georgia Papadogeorgou, Kosuke Imai, Jason Lyall, Fan Li, "Causal Inference with Spatio-temporal Data: Estimating the Effects of Airstrikes on Insurgent Violence in Iraq", arxiv:2003.13555
• Gordon J Ross, Tim Jones, "Understanding the Heavy Tailed Dynamics in Human Behavior", arxiv:1505.01547
• Catalin V. Rusu and Razvan V. Florian, "A New Class of Metrics for Spike Trains", Neural Computation 26 (2014): 306--348
• David Schnoerr, Ramon Grima, Guido Sanguinetti, "Cox process representation and inference for stochastic reaction-diffusion processes", Nature Communications 7 (2016): 11729, arxiv:1601.01972
• Dominic Schuhmacher, Aihua Xia, "A new metric between distributions of point processes", arxiv:0708.2777
• Victor Solo and Syed Ahmed Pasha, "Point-Process Principal Components Analysis via Geometric Optimization", Neural Computation 25 (2013): 101--122
• Wilson Truccolo, John P. Donoghue, "Nonparametric Modeling of Neural Point Processes via Stochastic Gradient Boosting Regression", Neural Computation 19 (2007): 672-705
• Ke Zhou, Hongyuan Zha, Le Song, "Learning Social Infectivity in Sparse Low-rank Networks Using Multi-dimensional Hawkes Processes", AISTATS 2013
• Lingjiong Zhu, "Nonlinear Hawkes Processes", arxiv:1304.7531