Point Processes

Last update: 02 Oct 2026 11:33
First version: 8 August 2018

Yet Another Inadequate Placeholder

Most good general books on stochastic processes cover at least simple point processes; I can particularly recommend Bartlett, Grimmett and Stirzaker, Guttorp, and Kallenberg

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

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 [Need to finish one of these years]
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