Simulation and Analysis of Random Fields

The package RandomFields allows for simulating various kinds of random fields, including anisotropic processes. Furthermore, algorithms for conditional simulation and simulation of max-stable random fields are provided. Additionally, the package includes tools for analysing spatial data: Hurst parameter, fractal dimension, empirical variogram, interactive fitting of parameters, LSQ and MLE estimation of parameters. Basic kriging procedures are also provided.

Starting with version 2.0, it also allows for the simulation of random fields that are non-stationary or multivariate or sophisticated space-time fields. fitvario allows for multivariate models and mixed effect models.

There are some changings in the definitions and in the output, see help("changings")


The following random fields and related functionalities are provided by the package.

  1. stationary and isotropic Gaussian random fields
    • CondSimu: conditional simulation
    • CovarianceFct,sophisticatedmodels: covariance functions and variogram models
    • EmpiricalVariogram: empirical variogram
    • GaussRF: simulation of Gaussian random fields; nice examples to get familiar with the simulation features of the package;
    • Kriging: simple and ordinary kriging
    • fitvario: variogram/covariance function fit by least squares, maximum likelihood and cross validation techniques
    • PrintMethodList: list of implemented simulation methods
    • ShowModels: interactive, graphical choice of models -- currently not available.

      Use ShowModels in version 1.3.x

    • soil: Soil physical and chemical data; theexamplegives a simple geostatistical analysis using features of the package
  2. stationary (and isotropic) max-stable random fields
    • CovarianceFct: covariance models for extremal Gaussian random fields
    • MaxStableRF: simulation of max-stable random fieldsNote: Simulation algorithm for Brown-Resnick processes will come up soon.
  3. stationary and isotropic Poisson random fields (not implemented yet) % \itemize{ % \item \code{%\link{ % PoissonRF%} % } : simulation of Poisson random fields % }

Data and example code:

  • soil: soil physical data
  • papers: code used in the papers published by the author
  • weather: UWME weather data
Functions used in diverse simulation methods:

Functions of general purpose:

    % \item \command{\link{eval.parameters}} : provides an interactive menu
  • fractal.dim: estimation of the fractal dimension
  • hurst: estimation of the Hurst parameter
  • Print: nice print function
  • regression: interactive regression plot
  • Locator,Readline:locatorandreadline, respectively, with storage and replay functionality
  • sleep.milli: sets the process into sleeping status

In the beta version, the following functionalities are currently not available:

  • ShowModels
  • numerical evaluation of the covariance function in tbm2
  • Harvard Rue's Markov fields


Many thanks to

    % \item Marco Oesting
  • R Core Team making available the algoithm for fft (fft.c) by Richard Singleton and advicing
  • Ben Pfaff, 12167 Airport Rd, DeWitt MI 48820, USA making available an algorithm for AVL trees (avltr*)
  • Peter Menck implemented the multivariate circulant embedding for version 2.0.
  • Yindeng Jiangjiangyindeng@gmail.comimplemented the circulant embedding methodscutoffandintrinsicin 2004 for the versions 1.2.
  • Martin Maechler, Paulo Ribeiro, and Tilmann Gneiting were proof-reading parts of the code and the help text for the versions 1.0.

Financial support

  • V1.0 has been financially supported by the German Federal Ministry of Research and Technology (BMFT) grant PT BEO 51-0339476C during 2000-03.
  • V1.0 has been financially supported by the EU TMR network ERB-FMRX-CT96-0095 on ``Computational and statistical methods for the analysis of spatial data'' in 1999.


Singleton, R.C. (1979). In Programs for Digital Signal Processing Ed.: Digital Signal Processing Committee and IEEE Acoustics, Speech, and Signal Processing Committe (1979) IEEE press.

  • RandomFields
Documentation reproduced from package RandomFields, version 2.0.71, License: GPL (>= 2)

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