Statistics on index sets with more than one dimension of support and, frequently, an implicit 2-norm.
Especially, processe on a continuous index set with continuous state and undirected interaction. 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 also curious about how spatial statistics generalise to high-dimensional fields such as fitness landscapes, loss functions, and embedding of network processes in space, and other stuff that doesn’t spring to mind.
This is not about Geographic Information Systems, although some of those do use spatial statistics.
Spatial point processes
Implementations of methods
- Anselin, L. (1995) Local Indicators of Spatial Association?LISA. Geographical Analysis, 27(2), 93–115. DOI.
- Anselin, L., Cohen, J., Cook, D., Gorr, W., & Tita, G. (2000) Spatial analyses of crime.
- Baddeley, A., Turner, R., Møller, J., & Hazelton, M. (2005) Residual analysis for spatial point processes (with discussion). Journal of the Royal Statistical Society: Series B (Statistical Methodology), 67(5), 617–666. DOI.
- Besag, J. (1974) Spatial Interaction and the Statistical Analysis of Lattice Systems. Journal of the Royal Statistical Society. Series B (Methodological), 36(2), 192–236.
- Besag, J. (1986) On the Statistical Analysis of Dirty Pictures. Journal of the Royal Statistical Society. Series B (Methodological), 48(3), 259–302.
- Brémaud, P., Massoulié, L., & Ridolfi, A. (2005) Power spectra of random spike fields and related processes. Advances in Applied Probability, 37(4), 1116–1146. DOI.
- Feng, Y., Liu, Y., & Batty, M. (2015) Modeling urban growth with GIS based cellular automata and least squares SVM rules: a case study in Qingpu–Songjiang area of Shanghai, China. Stochastic Environmental Research and Risk Assessment, 1–14. DOI.
- Fuentes, M. (2006) Testing for separability of spatial–temporal covariance functions. Journal of Statistical Planning and Inference, 136(2), 447–466. DOI.
- Huang, F., & Ogata, Y. (1999) Improvements of the Maximum Pseudo-Likelihood Estimators in Various Spatial Statistical Models. Journal of Computational and Graphical Statistics, 8(3), 510–530. DOI.
- Liu, C., Ray, S., & Hooker, G. (2014) Functional Principal Components Analysis of Spatially Correlated Data. arXiv:1411.4681 [Math, Stat].
- Mardia, K. V., & Marshall, R. J.(1984) Maximum likelihood estimation of models for residual covariance in spatial regression. Biometrika, 71(1), 135–146. DOI.
- Mohler, G. (2013) Modeling and estimation of multi-source clustering in crime and security data. The Annals of Applied Statistics, 7(3), 1525–1539. DOI.
- Møller, J., & Torrisi, G. L.(2007) The pair correlation function of spatial Hawkes processes. Statistics & Probability Letters, 77(10), 995–1003. DOI.
- Pollard, D. (2004, February 15) Hammersley-Clifford theorem for Markov random fields.
- Possolo, A. (1986) Estimation of binary Markov random fields.
- Rey, S. J., & Anselin, L. (2010) PySAL: A Python library of spatial analytical methods. In Handbook of applied spatial analysis (pp. 175–193). Springer
- Richardson, M., & Domingos, P. (2006) Markov logic networks. Machine Learning, 62(1–2), 107–136.
- Ripley, B. D.(1977) Modelling Spatial Patterns. Journal of the Royal Statistical Society. Series B (Methodological), 39(2), 172–212.
- Ripley, B. D.(1988) Statistical inference for spatial processes. . Cambridge [England]; New York: Cambridge University Press
- Saichev, A., & Sornette, D. (2006) Power law distribution of seismic rates: theory and data. The European Physical Journal B, 49(3), 377–401. DOI.
- Saparin, P. I., Gowin, W., Kurths, J., & Felsenberg, D. (1998) Quantification of cancellous bone structure using symbolic dynamics and measures of complexity. Physical Review E, 58(5), 6449–6459. DOI.
- Stein, M. L.(2005) Space-time covariance functions. Journal of the American Statistical Association, 100(469), 310–321. DOI.
- Szabó, G., Gergely, H., & Oborny, B. (2002) Generalized contact process on random environments. Physical Review E, 65(6), 66111. DOI.
- Whittle, P. (1954) On stationary processes in the plane. Biometrika, 41(3/4), 434–449.