Synonyms
Glossary
Correlation/covariance
Measures of similarity between observations
Geostatistics
A branch of spatial statistics
Isotropy
Property of covariance and variogram functions that make them is invariant under rotation of locations
Kriging
Method for linear unbiased prediction
Random field
A collection of random variables indexed by location
Stationarity
Property of random fields in which their mean and covariance functions are invariant under translation of locations
Variogram/semivariogram
Measures of dissimilarity between observations
Definition
Spatial statistics is a branch of statistics that studies methods to make inference based on data observed over spatial regions. In typical applications these regions are either 2- or 3-dimensional. The methodology is mostly aimed at accounting and modeling aspects of the so-called First Law of Geography: attributes from locations that are closer together are more closely related than...
References
Anselin L (1988) Spatial econometrics: methods and models. Kluwer, Dordrecht
Banerjee S, Carlin BP, Gelfand AE (2004) Hierarchical modeling and analysis for spatial data. Chapman & Hall/CRC, Boca Raton
Berke O (1999) Estimation and prediction in the spatial linear model. Water Air Soil Pollut 110:215–237
Bivand RS, Pebesba EJ, Gómez-Rubio V (2008) Applied spatial data analysis with R. Springer, New York
Chilès J-P, Delfiner P (1999) Geostatistics: modeling spatial uncertainty. Wiley, New York
Cliff AD, Ord JK (1981) Spatial processes: models and applications. Pion, London
Cressie NAC (1993) Statistics for spatial data. Wiley, New York
Daley D, Vere-Jones DJ (2003) Introduction to the theory of point processes, volume I: elementary theory and methods, 2nd edn. Springer, New York
Daley D, Vere-Jones DJ (2007) Introduction to the theory of point processes, volume II: general theory and structure, 2nd edn. Springer, New York
Diggle PJ (2003) Statistical analysis of spatial point patterns, 2nd edn. Arnold, New York
Diggle PJ, Ribeiro PJ (2007) Model-based geostatistics. Springer, New York
Gelfand AE, Diggle PJ, Guttorp P, Fuentes M (eds) (2010) Handbook of spatial statistics. Chapman & Hall/CRC, Boca Raton
Illian J, Penttinen A, Stoyan H, Stoyan D (2008) Statistical analysis and modelling of spatial point patterns. Wiley, Chichester
Journel AG, Huijbregts CJ (1978) Mining geostatistics. Academic, London
Le ND, Zidek JV (2006) Statistical analysis of environmental space-time processes. Springer, New York
LeSage JP, Pace RK (2009) Introduction to spatial econometrics. Chapman & Hall/CRC, Boca Raton
Li SZ (2009) Markov random field modeling in image analysis, 3rd edn. Springer, London
Matérn B (1986) Spatial variation. Lecture notes in statistics, 2nd edn. Springer, Berlin
Matheron G (1975) Random sets and integral geometry. Wiley, New York
Müller WG (2007) Collecting spatial data: optimum design of experiments for random fields, 3rd edn. Springer, Heidelberg
Nguyen HT (2006) An introduction to random sets. Chapman & Hall/CRC, Boca Raton
Ripley BD (1981) Spatial statistics. Wiley, New York
Rue H, Held L (2005) Gaussian Markov random fields: theory and applications. Chapman & Hall/CRC, Boca Raton
Schabenberger O, Gotway CA (2005) Statistical methods for spatial data analysis. Chapman & Hall/CRC, Boca Raton
Sjöstedt-De Luna S, Young A (2003) The bootstrap and kriging prediction intervals. Scand J Stat 30:175–192
Stein ML (1999) Interpolation of spatial data: some theory for kriging. Springer, New York
Wackernagel H (2010) Multivariate geostatistics: an introduction with applications, 3rd edn. Springer, Berlin
Yaglom AM (1987) Correlation theory of stationary and related random function I: basic results. Springer, New York
Acknowledgments
The authors thank Edgar Muñoz for producing Fig. 4. The first author was partially supported by National Science Foundation Grant HRD-0932339.
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Oliveira, V., Alexandre Trindade, A. (2016). Spatial Statistics. In: Alhajj, R., Rokne, J. (eds) Encyclopedia of Social Network Analysis and Mining. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7163-9_167-1
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DOI: https://doi.org/10.1007/978-1-4614-7163-9_167-1
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