Encyclopedia of Social Network Analysis and Mining

2018 Edition
| Editors: Reda Alhajj, Jon Rokne

Spatial Statistics

  • Victor OliveiraEmail author
  • A. Alexandre Trindade
Reference work entry
DOI: https://doi.org/10.1007/978-1-4939-7131-2_167




Measures of similarity between observations


A branch of spatial statistics


Property of covariance and variogram functions that make them is invariant under rotation of locations


Method for linear unbiased prediction

Random field

A collection of random variables indexed by location


Property of random fields in which their mean and covariance functions are invariant under translation of locations


Measures of dissimilarity between observations


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...

This is a preview of subscription content, log in to check access.



The authors thank Edgar Muñoz for producing Fig. 4. The first author was partially supported by National Science Foundation Grant HRD-0932339.


  1. Anselin L (1988) Spatial econometrics: methods and models. Kluwer, DordrechtzbMATHCrossRefGoogle Scholar
  2. Banerjee S, Carlin BP, Gelfand AE (2004) Hierarchical modeling and analysis for spatial data. Chapman & Hall/CRC, Boca RatonzbMATHGoogle Scholar
  3. Berke O (1999) Estimation and prediction in the spatial linear model. Water Air Soil Pollut 110:215–237CrossRefGoogle Scholar
  4. Bivand RS, Pebesba EJ, Gómez-Rubio V (2008) Applied spatial data analysis with R. Springer, New YorkzbMATHGoogle Scholar
  5. Chilès J-P, Delfiner P (1999) Geostatistics: modeling spatial uncertainty. Wiley, New YorkzbMATHCrossRefGoogle Scholar
  6. Cliff AD, Ord JK (1981) Spatial processes: models and applications. Pion, LondonzbMATHGoogle Scholar
  7. Cressie NAC (1993) Statistics for spatial data. Wiley, New YorkzbMATHGoogle Scholar
  8. Daley D, Vere-Jones DJ (2003) Introduction to the theory of point processes, volume I: elementary theory and methods, 2nd edn. Springer, New YorkzbMATHGoogle Scholar
  9. Daley D, Vere-Jones DJ (2007) Introduction to the theory of point processes, volume II: general theory and structure, 2nd edn. Springer, New YorkzbMATHGoogle Scholar
  10. Diggle PJ (2003) Statistical analysis of spatial point patterns, 2nd edn. Arnold, New YorkzbMATHGoogle Scholar
  11. Diggle PJ, Ribeiro PJ (2007) Model-based geostatistics. Springer, New YorkzbMATHGoogle Scholar
  12. Gelfand AE, Diggle PJ, Guttorp P, Fuentes M (eds) (2010) Handbook of spatial statistics. Chapman & Hall/CRC, Boca RatonzbMATHGoogle Scholar
  13. Illian J, Penttinen A, Stoyan H, Stoyan D (2008) Statistical analysis and modelling of spatial point patterns. Wiley, ChichesterzbMATHGoogle Scholar
  14. Journel AG, Huijbregts CJ (1978) Mining geostatistics. Academic, LondonGoogle Scholar
  15. Le ND, Zidek JV (2006) Statistical analysis of environmental space-time processes. Springer, New YorkzbMATHGoogle Scholar
  16. LeSage JP, Pace RK (2009) Introduction to spatial econometrics. Chapman & Hall/CRC, Boca RatonzbMATHCrossRefGoogle Scholar
  17. Li SZ (2009) Markov random field modeling in image analysis, 3rd edn. Springer, LondonzbMATHGoogle Scholar
  18. Matérn B (1986) Spatial variation. Lecture notes in statistics, 2nd edn. Springer, BerlinzbMATHCrossRefGoogle Scholar
  19. Matheron G (1975) Random sets and integral geometry. Wiley, New YorkzbMATHGoogle Scholar
  20. Müller WG (2007) Collecting spatial data: optimum design of experiments for random fields, 3rd edn. Springer, HeidelbergzbMATHGoogle Scholar
  21. Nguyen HT (2006) An introduction to random sets. Chapman & Hall/CRC, Boca RatonzbMATHCrossRefGoogle Scholar
  22. Ripley BD (1981) Spatial statistics. Wiley, New YorkzbMATHCrossRefGoogle Scholar
  23. Rue H, Held L (2005) Gaussian Markov random fields: theory and applications. Chapman & Hall/CRC, Boca RatonzbMATHCrossRefGoogle Scholar
  24. Schabenberger O, Gotway CA (2005) Statistical methods for spatial data analysis. Chapman & Hall/CRC, Boca RatonzbMATHGoogle Scholar
  25. Sjöstedt-De Luna S, Young A (2003) The bootstrap and kriging prediction intervals. Scand J Stat 30:175–192MathSciNetzbMATHCrossRefGoogle Scholar
  26. Stein ML (1999) Interpolation of spatial data: some theory for kriging. Springer, New YorkzbMATHCrossRefGoogle Scholar
  27. Wackernagel H (2010) Multivariate geostatistics: an introduction with applications, 3rd edn. Springer, BerlinzbMATHGoogle Scholar
  28. Yaglom AM (1987) Correlation theory of stationary and related random function I: basic results. Springer, New YorkzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Management Science and StatisticsThe University of Texas at San AntonioSan AntonioUSA
  2. 2.Department of Mathematics and StatisticsTexas Tech UniversityLubbockUSA

Section editors and affiliations

  • Suheil Khoury
    • 1
  1. 1.American University of SharjahSharjahUnited Arab Emirates