spatialCopula: A Matlab toolbox for copula-based spatial analysis

  • Hannes KaziankaEmail author
Original Paper


The spatialCopula toolbox contains a set of Matlab functions that provides utilities for copula-based analysis of spatially referenced data, a topic which has re cently attracted much attention in spatial statistics. These tools have been developed to support the work flow in parameter estimation, spatial interpolation and visualization. They offer flexible and user-friendly software for dealing with non-Gaussian and extreme value data that possibly contain a spatial trend or geometric anisotropy. The objective of this paper is to give an introduction to the concept behind the software and to outline the functionality of the toolbox. We illustrate its usefulness by analyzing a data set here referred to as the Gomel data set, which includes moderately skewed radioactivity measurements in the region of Gomel, Belarus. The source codes are freely available in Matlab language on the author’s website (


Copula Spatial modelling Spatial interpolation Matlab 


  1. Banerjee S, Gelfand A, Sirmans C (2003) Directional rates of change under spatial process models. J Am Stat Assoc 98:946–954CrossRefGoogle Scholar
  2. Bárdossy A (2006) Copula-based geostatistical models for groundwater quality parameters. Water Resour Res 42:W11416. doi: 10.1029/2005WR004754
  3. Bárdossy A, Li J (2008) Geostatistical interpolation using copulas. Water Resour Res 44:W07412. doi: 10.1029/2007WR006115
  4. Bivand R, Pebesma E, Gomez-Rubio V (2008) Applied spatial data analysis with R. Springer, BerlinGoogle Scholar
  5. Chorti A, Hristopulos D (2008) Non-parametric identification of anisotropic (elliptic) correlations in spatially distributed data sets. IEEE Trans Signal Process 56:4738–4751CrossRefGoogle Scholar
  6. De Oliveira V, Kedem B, Short D (1997) Bayesian prediction of transformed Gaussian random fields. J Am Stat Assoc 92:1422–1433CrossRefGoogle Scholar
  7. Diggle P, Ribeiro P (2007) Model-based geostatistics. Springer, New YorkGoogle Scholar
  8. Gaudard M, Karson M, Linder E, Sinha D (1999) Bayesian spatial prediction. Environ Ecol Stat 6:147–171CrossRefGoogle Scholar
  9. Gelman A, Rubin D (1992) Inference from iterative simulation using multiple sequences (with discussion). Stat Sci 7:457–511CrossRefGoogle Scholar
  10. Goovaerts P (2001) Geostatistical modelling of uncertainty in soil science. Geoderma 103:3–26CrossRefGoogle Scholar
  11. Joe H (1997) Multivariate models and dependence concepts. Chapman & Hall/CRC, Boca RatonCrossRefGoogle Scholar
  12. Kazianka H, Pilz J (2010a) Spatial interpolation using copula-based geostatistical models. In: Atkinson P, Lloyd C (eds) geoENV VII—Geostatistics for environmental applications. Springer, Berlin, pp 307–320CrossRefGoogle Scholar
  13. Kazianka H, Pilz J (2010b) Copula-based geostatistical modeling of continuous and discrete data including covariates. Stoch Environ Res Risk Assess 24:661–673CrossRefGoogle Scholar
  14. Kazianka H, Pilz J (2011) Bayesian spatial modeling and interpolation using copulas. Comp Geosci 37:310–319CrossRefGoogle Scholar
  15. Kazianka H, Pilz J (2012) Objective Bayesian analysis of spatial data with uncertain nugget and range parameters. Can J Stat (in press)Google Scholar
  16. Pebesma E, Cornford D, Dubois G, Heuvelink G, Hristopoulos D, Pilz J, Stoehlker U, Morin G, Skoien J (2011) INTAMAP: the design and implementation of an interoperable automated interpolation web service. Comp Geosci 37:343–352CrossRefGoogle Scholar
  17. Pilz J, Spöck G (2008) Why do we need and how should we implement Bayesian kriging methods. Stoch Environ Res Risk Assess 22:621–632CrossRefGoogle Scholar
  18. Sklar A (1959) Fonctions de repartition a n dimensions et leurs marges. Publ Inst Stat Univ Paris 8:229–231Google Scholar
  19. Stein M (1999) Interpolation of spatial data: some theory for kriging. Springer, New YorkCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of KlagenfurtKlagenfurtAustria

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