Spatial-Temporal Statistics

Last update: 21 Apr 2025 21:17
First version: 29 December 2012

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That is, statistics for random variables spread out in space and evolving in time; this is not quite the intersection of time series and spatial statistics...

This notebook is currently grossly undersupplied with recommendations, but I don't have time at the moment to add more. Soon, with any luck...

To look into: parts of the applied math community seem to be very into "dynamic mode decompositions"; from what I can tell, this just means ignoring the actual dynamics to fit a big VAR(1), and then prophesying upon the eigenvectors. Is there more to it?

See also:
• Agent-Based Modeling
• Cellular Automata
• Factor Models for High-Dimensional Time Series and Spatio-Temporal Data
• Interacting Particle Systems
• Optimal Linear Prediction and Estimation
• Pattern Formation
• Point Processes
• Spatial Patterns in Crime, Especially Clustering/Concentration
• Synchronization

Recommended, big picture:
• Noel A. C. Cressie and Christopher K. Wikle, Statistics for Spatio-Temporal Data
• Gidon Eshel, Spatiotemporal Data Analysis [Review, with some caveats/tempered enthusiasm]
• Carlo Gaetan and Xavier Guyon, Spatial Statistics and Modeling
• Peter Guttorp, Stochastic Modeling of Scientific Data

Recommended, close-ups (very misc.):
• Ole E. Barndorff-Nielsen, Fred Espen Benth and Almut E. D. Veraart, Ambit Stochastics
• Niccolò Dalmasso, Robin Dunn, Benjamin LeRoy and Chad Schafer, "A Flexible Pipeline for Prediction of Tropical Cyclone Paths", arxiv:1906.08832
• Bärbel Finkenstädt, Leonhard Held and Valerie Isham (eds.), Statistical Methods for Spatio-Temporal Systems
• H. Jänicke and G. Scheuermann, "Steady visualization of the dynamics in fluids using $\epsilon$-machines", Computers and Graphics 33 (2009): 597--606
• Heike Jänicke, Alexander Wiebel, Gerik Scheuermann and Wolfgang Kollmann, "Multifield Visualization Using Local Statistical Complexity", IEEE Transactions on Visualization and Computer Graphics 13 (2007): 1384--1391 [PDF]
• Jian Liu, Zhen-Su She, Hongyu Guo, Liang Li and Qi Ouyang, "Hierarchical structure description of spatiotemporal chaos", Physical Review E 70 (2004): 036215 = nlin.PS/0408024
• Ulrich Parlitz and Christian Merkwirth, "Prediction of Spatiotemporal Time Series Based on Reconstructed Local States," Physical Review Letters 84 (2000): 1890--1893
• Jonathan R. Stroud, Peter Müller and Bruno Sansó, "Dynamic Models for Spatio-Temporal Data", Journal of the Royal Statistical Society B 63 (2001): 673--689 [PDF via Prof. Stroud; PDF via Prof. Sansó]
• Gyorgy Szabo, Hajnalka Gergely, and Beata Oborny, "Generalized contact process on random environments," cond-mat/0202461
• Scott M. Zoldi and Henry S. Greenside, "Karhunen-Loève Decomposition of Extensive Chaos," chao-dyn/9610007 ["to appear in PRL" --- presumably has by now]
• Scott M. Zoldi, Jun Liu, Kapil M. S. Bajaj, Henry S. Greenside and Guenter Ahlers, "Extensive Scaling and Nonuniformity of the Karhunen-Loève Decomposition for the Spiral-Defect Chaos State," chao-dyn/9808006

Modesty forbids me:
• Georg M. Goerg and CRS [Self-popularization]
  • "LICORS: Light Cone Reconstruction of States for Non-parametric Forecasting of Spatio-Temporal Systems", arxiv:1206.2398
  • "Mixed LICORS: A Nonparametric Algorithm for Predictive State Reconstruction", arxiv:1211.3760
• George D. Montanez and CRS, "The LICORS Cabinet: Nonparametric Algorithms for Spatio-temporal Prediction", International Joint Conference on Neural Networks 2017 [IJCNN 2017], arxiv:1506.02686
• CRS, "Optimal Nonlinear Prediction of Random Fields on Networks," Discrete Mathematics and Theoretical Computer Science vol. "AB(DMCS)" (2003), pp. 11--30 = math.PR/0305160
• CRS, lecture notes for 36-467, Data over Space and Time
• CRS, Robert Haslinger, Jean-Baptiste Rouquier, Kristina Lisa Klinkner and Cristopher Moore, "Automatic Filters for the Detection of Coherent Structure in Spatiotemporal Systems", Physical Review E 73 (2006): 036104, arxiv:nlin.CG/0508001 [Self-popularization]

To read, historical interest:
• Aitor Anduaga, Politics, Statistics and Weather Forecasting, 1840--1910: Taming the Weather

To read:
• Markus Abel, "Nonparametric modeling and spatiotemporal dynamical systems," nlin.PS/0202058
• Sivan Aldor-Noiman, Lawrence D. Brown, Emily B. Fox, Robert A. Stine, "Spatio-Temporal Low Count Processes with Application to Violent Crime Events", arxiv:1304.5642
• Alberto Alvarez, Cristobal Lopez, Margalida Riera, Emilio Hernandez-Garcia and Joaquin Tintore, "Forecasting the SST space-time variability of the Alboran Sea with genetic algorithms," chao-dyn/9911012 = Geophysical Research Letters 27 (2000): 739--742
• John A. D. Aston, Claudia Kirch, "Evaluating stationarity via change-point alternatives with applications to fMRI data", Annals of Applied Statistics 6 (2012): 1906--1948, arxiv:1301.2894
• Andrew W. Baggaley, Richard J. Boys, Andrew Golightly, Graeme R. Sarson, and Anvar Shukurov, "Inference for population dynamics in the Neolithic period", Annals of Applied Statistics 6 (2012): 1352--1376
• Yun Bai, Peter X.-K. Song, T. E. Raghunathan, "Joint composite estimating functions in spatiotemporal models", Journal of the Royal Statistical Society B forthcoming (2012)
• Wanfang Chen, Marc G. Genton and Ying Sun, "Space-Time Covariance Structures and Models", Annual Review of Statistics and Its Applications forthcoming (2021)
• Piero Cipriani and Antonio Politi, "An open-system approach for the characterization of spatio-temporal chaos," nlin.CD/0301003
• Robert Alan Clements, Frederic Paik Schoenberg, and Danijel Schorlemmer, "Residual analysis methods for space-time point processes with applications to earthquake forecast models in California", Annals of Applied Statistics 5 (2011): 25499--2571, arxiv:1202.6487,
• Noel Cressie, Tao Shi, and Emily L. Kang, "Fixed Rank Filtering for Spatio-Temporal Data", Journal of Computational and Graphical Statistics (2010) forthcoming
• Jorn Davidsen, Peter Grassberger and Maya Paczuski, "Networks of Recurrent Events, a Theory of Records, and an Application to Finding Causal Signatures in Seismicity", physics/0701190
• S. De Iaco, M. Palma and D. Posa, "Modeling and prediction of multivariate space-time random fields", Computational Statistics and Data Analysis 48 (2004): 525--547
• Peter J. Diggle, Statistical Analysis of Spatial and Spatio-Temporal Point Patterns
• Seth Flaxman, Michael Chirico, Pau Pereira, Charles Loeffler, "Scalable high-resolution forecasting of sparse spatiotemporal events with kernel methods: a winning solution to the NIJ "Real-Time Crime Forecasting Challenge" ", arxiv:1801.02858
• Seth Flaxman, Daniel Neill, Alex Smola, "Correlates of homicide: new space/time interaction tests for spatiotemporal point processes", Heinz College (CMU) Tech Report 409
• Thaís C. O. Fonseca and Mark F. J. Steel, "Non-Gaussian spatiotemporal modelling through scale mixing", Biometrika 98 (2011): 761--774
• Gerson Francisco and Paulsamy Muruganandam, "Local dimension and finite time prediction in spatiotemporal chaotic systems," Physical Review E 67 (2003): 066204, nlin.CD/0212015
• Edith Gabriel, Barry S. Rowlingson, Peter J. Diggle, "stpp: An R Package for Plotting, Simulating and Analyzing Spatio-Temporal Point Patterns", Journal of Statistical Software 53 (2010): 2
• Alan E. Gelfand, Peter J. Diggle, Montserrat Fuentes and Peter Guttorp (eds.), Handbook of Spatial Statistics
• Henry S. Greenside, "Spatiotemporal Chaos in Large Systems: The Scaling of Complexity with Size," chao-dyn/9612004
• Patrick Harrington and Alfred Hero, "Spatio-Temporal Graphical Model Selection", arxiv:1004.2304
• Mevin B. Hooten and Christopher K. Wikle, "Statistical Agent-Based Models for Discrete Spatio-Temporal Systems", Journal of the American Statistical Association 105 (2010): 236--248
• L. Ippoliti, P. Valentini, D. Gamerman, "Space-time modelling of coupled spatiotemporal environmental variables", Journal of the Royal Statistical Society C 61 (2012): 175--200
• Kota Katanoda, Yasumasa Matsuda and Morihiro Sugishita, "A Spatio-temporal Regression Model for the Analysis of Functional MRI Data", NeuroImage 17 (2002): 1415--1428
• Nhu D. Le and James V. Zidek, Statistical Analysis of Environmental Space-Time Processes
• Cristobal Lopez and Emilio Hernandez-Garcia, "Low-dimensional dynamical system model for observed coherent structures in ocean satellite data," nlin.CD/0009039
• Cristobal Lopez, Alberto Alvarez and Emilio Hernandez-Garcia, "Forecasting confined spatiotemporal chaos with genetic algorithms," nlin.CD/0003060 = Physical Review Letters 85 (2000): 2300--2303
• Zudi Lu, Dag Johan Steinskog, Dag Tjostheim and Qiwei Yao, "Adaptively Varying-Coefficient Spatiotemporal Models", Journal of the Royal Statistical Society B 71 (2009): 859--880 [PDF preprint]
• Andrew J. Majda and Marcus J. Grote, "Explicit off-line criteria for stable accurate time filtering of strongly unstable spatially extended systems", Proceedings of the National Academy of Sciences (USA) 104 (2007): 1124--1129
• S. Mandelj, I. Grabec, E. Govekar, "Statistical approach to modeling of spatiotemporal dynamics," International Journal of Bifurcations and Chaos 11 (2001): 2731--2738
• Chiara Mocenni, Angelo Facchini and Antonio Vicino, "Identifying the dynamics of complex spatio-temporal systems by spatial recurrence properties", Proceedings of the National Academy of Sciences 107 (2010): 8097--8102
• Jose-Maria Montero, Gema Fernandez-Aviles and Jorge Mateu, Spatial and Spatio-Temporal Geostatistical Modeling and Kriging
• T. J. Muller and J. Timmer, "Fitting parameters in partial differential equations from partially observed noisy data," Physica D 171 (2002): 1--7
• Girish Nathan and Gemunu Gunaratne, "Set of measures to analyze the dynamics of nonequilibrium structures", Physical Review E 71 (2005): 035101(R)
• David O'Sullivan George L. W. Perry, Spatial Simulation: Exploring Pattern and Process
• Edward Ott, Brian R. Hunt, Istvan Szunyogh, Matteo Corazza, Eugenia Kalnay, D. J. Patil, and James A. Yorke, "Exploiting Local Low Dimensionality of the Atmospheric Dynamics for Efficient Ensemble Kalman Filtering," physics/0203058
• E. Ott, B. R. Hunt, I. Szunyogh, A. V. Zimin, E. J. Kostelich, M. Corazza, E. Kalnay, D.J. Patil and J.A. Yorke, "Estimating the state of large spatio-temporally chaotic systems", Physics Letters A 330 (2004): 365--370
• 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
• Nita Parekh, V. Ravi Kumar and B. D. Kulkarni, "Synchronization and Control of Spatiotemporal Chaos using Time-Series Data from Local Regions," chao-dyn/9711002
• Andrew J. Peters, Simon X. Chen and Takaki Komiyama, "Emergence of reproducible spatiotemporal activity during motor learning", Nature 510 (2014): 263--267
• Nico Piatkowski, Sangkyun Lee and Katharina Morik, "Spatio-temporal random fields: compressible representation and distributed estimation", Machine Learning 93 (2013): 115--139
• MarcAurelio Ranzato, Arthur Szlam, Joan Bruna, Michael Mathieu, Ronan Collobert, Sumit Chopra, "Video (language) modeling: a baseline for generative models of natural videos", arxiv:1412.6604
• Rachid Senoussi and Emilio Porcu, "Nonstationary space-time covariance functions induced by dynamical systems", Scandinavian Journal of Statistics 49 (2022): 211--235
• Michael Sherman, Spatial Statistics and Spatio-Temporal Data: Covariance Functions and Directional Properties
• Fabio Sigrist, Hans R. Künsch, and Werner A. Stahel, "A dynamic nonstationary spatio-temporal model for short term prediction of precipitation", Annals of Applied Statistics 6 (2012): 1452--1477
• A. Sitz, J. Kurths, and H. U. Voss, "Identification of nonlinear spatiotemporal systems via partitioned filtering", Physical Review E 68 (2003): 016202
• Nitish Srivastava, Elman Mansimov, Ruslan Salakhutdinov, "Unsupervised Learning of Video Representations using LSTMs", arxiv:1502.04681
• M. L. Stein, "Space-Time Covariance Functions", Technical Report No. 4, University of Chicago Center for Integrating Statistical and Environmental Sciences (May 2003) [PDF]
• Martin Treiber and Dirk Helbing, "An adaptive smoothing method for traffic state identification from incomplete information," cond-mat/0210050
• H. Voss, M. J. Bünner and M. Abel, "The Identification of Continuous, Spatiotemporal Systems," Physical Review E 57 (1998): 2820
• X. Xia and H. Leung, "Nonlinear Spatial-Temporal Prediction Based on Optimal Fusion", IEEE Transactions on Neural Networks 17 (2006): 975--988
• Jun-Ming Xu, Aniruddha Bhargava, Robert Nowak, and Xiaojin Zhu, "Socioscope: Spatio-Temporal Signal Recovery from Social Media" [PDF]
• Dongchuan Yu and Ulrich Parlitz, "Inferring local dynamics and connectivity of spatially extended systems with long-range links based on steady-state stabilization", Physical Review E 82 (2010): 026108
• Andrew Zammit-Mangion, Noel Cressie, "FRK: An R Package for Spatial and Spatio-Temporal Prediction with Large Datasets", arxiv:1705.08105
• Andrew Zammit-Mangion, Michael Dewar, Visakan Kadirkamanathan, and Guido Sanguinetti, "Point process modelling of the Afghan War Diary", Proceedings of the National Academy of Sciences (USA) 109 (2012): 12414--12419
• Chuan Zhang, Kentaroh Takagaki, Xiaoying Huang, Steven J. Schiff, Jian-Young Wu, "A geometric method for spatiotemporal coherent structure analysis", arxiv:1212.5843

To write:
• Co-conspirators + CRS, "A Nonparametric Sieve Bootstrap for Spatio-Temporal Data"
• Co-conspirators + CRS, "Universal Pattern Discovery with Local Statistical Complexity"
• Co-conspirators + CRS, "Local Statistical Complexity: Estimation and Uncertainty"
• CRS, Data over Space and Time

Notebooks :