The Living Thing / Notebooks : Spatial processes and statistics thereof

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

A particular sub-case combining point processes with spatial statics, now with its own notebook

Implementations of methods

spatstat
  1. Classic general-purpose spatial data anlaysis.
PySAL
Python. Library of statistical functions for continuous-state spatial processes.
PASSaGE
Python. GUI full of statistical analyses.

Refs

Anse95
Anselin, L. (1995) Local Indicators of Spatial Association?LISA. Geographical Analysis, 27(2), 93–115. DOI.
ACCG00
Anselin, L., Cohen, J., Cook, D., Gorr, W., & Tita, G. (2000) Spatial analyses of crime.
BTMH05
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.
Besa74
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.
Besa86
Besag, J. (1986) On the Statistical Analysis of Dirty Pictures. Journal of the Royal Statistical Society. Series B (Methodological), 48(3), 259–302.
BrMR05
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.
FeLB15
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.
Fuen06
Fuentes, M. (2006) Testing for separability of spatial–temporal covariance functions. Journal of Statistical Planning and Inference, 136(2), 447–466. DOI.
HuOg99
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.
LiRH14
Liu, C., Ray, S., & Hooker, G. (2014) Functional Principal Components Analysis of Spatially Correlated Data. arXiv:1411.4681 [Math, Stat].
MaMa84
Mardia, K. V., & Marshall, R. J.(1984) Maximum likelihood estimation of models for residual covariance in spatial regression. Biometrika, 71(1), 135–146. DOI.
Mohl13
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.
MøTo07
Møller, J., & Torrisi, G. L.(2007) The pair correlation function of spatial Hawkes processes. Statistics & Probability Letters, 77(10), 995–1003. DOI.
Poll04
Pollard, D. (2004, February 15) Hammersley-Clifford theorem for Markov random fields.
Poss86
Possolo, A. (1986) Estimation of binary Markov random fields.
ReAn10
Rey, S. J., & Anselin, L. (2010) PySAL: A Python library of spatial analytical methods. In Handbook of applied spatial analysis (pp. 175–193). Springer
RiDo06
Richardson, M., & Domingos, P. (2006) Markov logic networks. Machine Learning, 62(1–2), 107–136.
Ripl77
Ripley, B. D.(1977) Modelling Spatial Patterns. Journal of the Royal Statistical Society. Series B (Methodological), 39(2), 172–212.
Ripl88
Ripley, B. D.(1988) Statistical inference for spatial processes. . Cambridge [England]; New York: Cambridge University Press
SaSo06
Saichev, A., & Sornette, D. (2006) Power law distribution of seismic rates: theory and data. The European Physical Journal B, 49(3), 377–401. DOI.
SGKF98
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.
Stei05
Stein, M. L.(2005) Space-time covariance functions. Journal of the American Statistical Association, 100(469), 310–321. DOI.
SzGO02
Szabó, G., Gergely, H., & Oborny, B. (2002) Generalized contact process on random environments. Physical Review E, 65(6), 66111. DOI.
Whit54
Whittle, P. (1954) On stationary processes in the plane. Biometrika, 41(3/4), 434–449.