Dr. Benedikt Gräler

52°North Spatial Information Research GmbH
Martin-Luther-King-Weg 24
48155 Muenster, Germany




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spatial copulas

copulas as a tool

The following talk gives a brief introduction to copulas and illustrates how copulas can be used to explore and model multi-variate processes. My copulatheque allows to interactively explore different copula families including one representation of a bivariate spatial copula. The slides provide as well a few R-code snippest on how to get started with copulas in R using the packages copula and spcopula.

Pasting the following line to your R-console prompt will install the latest version of the package spcopula:
install.packages("spcopula", repos="http://R-Forge.R-project.org")


spatial copulas

The slides of the following introductive course on spatial copulas have been composed for an one week block course for Geoinformatics master and PhD students. All sections are accompanied with some exercises. Their solutions have so far only been implemented using the statistical programming language R with some additional packages (copula, spcopula, gstat, evd).

This is the first version of the course held in February 2011. Please, do not hesitate to contact me if you have questions, comments or found an error.



In chapter one I give some background theory on Probability Theory and Statistics including one section on Extreme Value Distributions.


Co-Kriging and Indicator-Kriging

The second chapter briefly reviews the classical Co-Kriging and Indicator-Kriging approaches. Copulas can then be used to substitute the covariance matrix in Indicator-Kriging


Introduction to Copulas

An introduction to copulas and spatial copulas is given in chapter three. The definitions, some properties and estimation procedures can be found in these sections.


Applied Copulas

Chapter four introduces some possibilities on how to use copulas in the spatial domain.


Amazon Copula

Chapter five illustrates a small example from a case study conducted on the deforestation of the Brazilian Amazon. The results were presented on the GeoChange Research Symposium. The slides include some copulas suitable for zero-inflated data.

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