Statistics on fields with index sets of more than one dimension of support and, frequently, an implicit 2-norm.
Especially, for processes on a continuous index set with continuous state and undirected interaction. Usually not calculated on fancy manifolds, but plain old euclidean space. Lattice models are frequently considered spatial statistics, but more arbitrary graph structures usually get filed under undirected graphical models/random fields. For spatial point processes I will make a new notebook. There are many other random fields we might also wish to infer that also relate to spatial index sets, and these can be taxonomised as I notice their existence.
I'm curious about how spatial statistics generalise to high-dimensional fields such as fitness landscapes, loss functions, and embedding of network processes in space…
This is not about Geographic Information Systems, or other spatial data viz although presumably some of those do use spatial statistics.
Spatial point processes
A particular sub-case combining point processes with spatial statics, now with its own notebook
Implementations of methods
Spatstat is the reference general-purpose spatial data analysis. based on R.
PySAL Python. Library of statistical functions for continuous-state spatial processes.
Passage is also Python. GUI full of statistical analyses.
- Stei08: Michael L. Stein (2008) A modeling approach for large spatial datasets. Journal of the Korean Statistical Society, 37(1), 3–10. DOI
- Abra97: Petter Abrahamsen (1997) A review of Gaussian random fields and correlation functions
- StCW04: Michael L. Stein, Zhiyi Chi, Leah J. Welty (2004) Approximating likelihoods for large spatial data sets. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 66(2), 275–296. DOI
- Poss86: Antonio Possolo (1986) Estimation of binary Markov random fields
- LiRH14: Chong Liu, Surajit Ray, Giles Hooker (2014) Functional Principal Components Analysis of Spatially Correlated Data. ArXiv:1411.4681 [Math, Stat].
- Poll04: Dave Pollard (2004) Hammersley-Clifford theorem for Markov random fields
- DoJo94: David L. Donoho, Jain M. Johnstone (1994) Ideal spatial adaptation by wavelet shrinkage. Biometrika, 81(3), 425–455. DOI
- HuOg99: Fuchun Huang, Yosihiko Ogata (1999) Improvements of the Maximum Pseudo-Likelihood Estimators in Various Spatial Statistical Models. Journal of Computational and Graphical Statistics, 8(3), 510–530. DOI
- NoLi13: W. Nowak, A. Litvinenko (2013) Kriging and Spatial Design Accelerated by Orders of Magnitude: Combining Low-Rank Covariance Approximations with FFT-Techniques. Mathematical Geosciences, 45(4), 411–435. DOI
- Anse95: Luc Anselin (1995) Local Indicators of Spatial Association – LISA. Geographical Analysis, 27(2), 93–115. DOI
- RiDo06: Matthew Richardson, Pedro Domingos (2006) Markov logic networks. Machine Learning, 62(1–2), 107–136.
- MaMa84: K. V. Mardia, R. J. Marshall (1984) Maximum likelihood estimation of models for residual covariance in spatial regression. Biometrika, 71(1), 135–146. DOI
- Mohl13: George Mohler (2013) Modeling and estimation of multi-source clustering in crime and security data. The Annals of Applied Statistics, 7(3), 1525–1539. DOI
- Ripl77: B. D. Ripley (1977) Modelling Spatial Patterns. Journal of the Royal Statistical Society. Series B (Methodological), 39(2), 172–212.
- Whit54: P Whittle (1954) On stationary processes in the plane. Biometrika, 41(3/4), 434–449.
- Besa86: Julian Besag (1986) On the Statistical Analysis of Dirty Pictures. Journal of the Royal Statistical Society. Series B (Methodological), 48(3), 259–302.
- RoAn11: Michael S. Rosenberg, Corey Devin Anderson (2011) PASSaGE: Pattern Analysis, Spatial Statistics and Geographic Exegesis Version 2: PASSaGE. Methods in Ecology and Evolution, 2(3), 229–232. DOI
- SaSo06: A. Saichev, D. Sornette (2006) Power law distribution of seismic rates: theory and data. The European Physical Journal B, 49(3), 377–401. DOI
- BrMR05: Pierre Brémaud, Laurent Massoulié, Andrea Ridolfi (2005) Power spectra of random spike fields and related processes. Advances in Applied Probability, 37(4), 1116–1146. DOI
- Mack95: David J. C. Mackay (1995) Probable networks and plausible predictions — a review of practical Bayesian methods for supervised neural networks. Network: Computation in Neural Systems, 6(3), 469–505. DOI
- ReAn10: Sergio J. Rey, Luc Anselin (2010) PySAL: A Python library of spatial analytical methods. In Handbook of applied spatial analysis (pp. 175–193). Springer
- SGKF98: Peter I Saparin, Wolfgang Gowin, Jürgen Kurths, Dieter Felsenberg (1998) Quantification of cancellous bone structure using symbolic dynamics and measures of complexity. Physical Review E, 58(5), 6449–6459. DOI
- BTMH05: A. Baddeley, R. Turner, J. Møller, M. Hazelton (2005) Residual analysis for spatial point processes (with discussion). Journal of the Royal Statistical Society: Series B (Statistical Methodology), 67(5), 617–666. DOI
- Stei05: Michael L Stein (2005) Space-time covariance functions. Journal of the American Statistical Association, 100(469), 310–321. DOI
- ACCG00: Luc Anselin, Jacqueline Cohen, David Cook, Wilpen Gorr, George Tita (2000) Spatial analyses of crime.
- Besa74: Julian Besag (1974) Spatial Interaction and the Statistical Analysis of Lattice Systems. Journal of the Royal Statistical Society. Series B (Methodological), 36(2), 192–236.
- BaRT16: Adrian Baddeley, Ege Rubak, Rolf Turner (2016) Spatial point patterns: methodology and applications with R. Boca Raton ; London ; New York: CRC Press, Taylor & Francis Group
- Ripl88: Brian D Ripley (1988) Statistical inference for spatial processes. Cambridge [England]; New York: Cambridge University Press
- SuSt16: Ying Sun, Michael L. Stein (2016) Statistically and Computationally Efficient Estimating Equations for Large Spatial Datasets. Journal of Computational and Graphical Statistics, 25(1), 187–208. DOI
- Fuen06: Montserrat Fuentes (2006) Testing for separability of spatial–temporal covariance functions. Journal of Statistical Planning and Inference, 136(2), 447–466. DOI
- MøTo07: Jesper Møller, Giovanni Luca Torrisi (2007) The pair correlation function of spatial Hawkes processes. Statistics & Probability Letters, 77(10), 995–1003. DOI