RandomFields (version 3.0.62)

RandomFields-package: Simulation and Analysis of Random Fields

Description

The package RandomFields offers various tools for

1. simulation

of different kinds of random fields, including

• multivariate, spatial, spatio-temporal Gaussian random fields,
• Poisson fields, binary fields, Chi2 fields, t fields and
• max-stable fields.

It can also deal with non-stationarity and anisotropy of these processes and conditional simulation (for Gaussian random fields, currently). model estimation (ML) and inference (tests) for regionalizd variables and data analysis,

model estimation for (geostatistical) linear (mixed) models

url

http://ms.math.uni-mannheim.de/de/publications/software/

bold

intermediate updates

Changings

A list of major changings from Version 2 to Version 3 can be found in MajorRevisions.

Changings lists some further changings, in particular of argument and argument names.

Update

Current updates are available through http://ms.math.uni-mannheim.de/de/publications/software.

Contributions

• Contributions to version 3.0 and following: Felix Ballani (TU Bergakademie Freiberg; Poisson Polygons, 2014) Daphne Boecker (Univ. Goettingen; RFgui, 2011) Katharina Burmeister (Univ. Goettingen; testing, 2012) Sebastian Engelke (Univ. Goettingen; RFempiricalvariogram, 2011-12) Sebastian Gross (Univ. Goettingen; tilde formulae, 2011) Alexander Malinowski (Univ. Mannheim; S3, S4 classes 2011-13) Juliane Manitz (Univ. Goettingen; testing, 2012) Johannes Martini (Univ. Goettingen; RFempiricalvariogram, 2011-12) Ulrike Ober (Univ. Goettingen; help pages, testing, 2011-12) Marco Oesting (Univ. Mannheim; Brown-Resnick processes, Kriging, Trend, 2011-13) Paulo Ribeiro (Unversidade Federal do Parana; code adopted fromgeoR, 2014) Kirstin Strokorb (Univ. Mannheim; help pages, 2011-13)
• Contributions to version 2.0 and following: Peter Menck (Univ. Goettingen; multivariate circulant embedding) R Core Team, Richard Singleton (fft.c and advice)
• Contributions to version 1 and following: Ben Pfaff, 12167 Airport Rd, DeWitt MI 48820, USA making available an algorithm for AVL trees (avltr*)

Thanks

Patrick Brown : comments on Version 3 Paulo Riberio : comments on Version 1 Martin Maechler : advice for Version 1

Financial support

• V3.0 has been financially supported by the German Science Foundation (DFG) through the Research Training Group 1953Statistical Modeling of Complex Systems and Processes --- Advanced Nonparametric Approaches(2013-2018).
• V3.0 has been financially supported by Volkswagen Stiftung within the projectWEX-MOP(2011-2014).
• Alpha versions for V3.0 have been financially supported by the German Science Foundation (DFG) through the Research Training Groups 1644Scaling problems in Statisticsand 1023Identification in Mathematical Models(2008-13).
• 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.

Details

The following features are provided by the package:

1. Simulation
   • RFsimulate: Simulation of random fields, including conditional simulation. For a list of all covariance functions and variogram models seeRMmodel. Useplotfor visualisation of the result.
2. Estimation of parameters (for second-order random fields)
   • RFfit: general function for estimating parameters; (for Gaussian random fields)
   • RFhurst: estimation of the Hurst parameter
   • RFfractaldim: estimation of the fractal dimension
   • RFempiricalvariogram: calculates the empirical variogram
3. Prediction (for second-order random fields)
   • RFinterpolate: kriging, including imputing
4. Inference (for Gaussian random fields)
   • RFcrossvalidate: cross validation
   • RFratiotest: likelihood ratio test
   • AIC,AICc,BIC,anova,logLik
5. Models
   • For a list of covariance and variogram models --e.g. forgeostatisticalpurposes-- seeRMmodel. More sophisticated models and covariance function operators are included.
   • To apply the offered package procedures tomixed models-- e.g. appearing in genetical data analysis-- seeRFformula.
   • definite models are evaluated byRFcov,RFvariogramandRFcovmatrix. For a quick impression useplot(model).
   • non-definte models are evaluated byRFfctnandRFcalc
6. Data and example studies: Some data sets and published code are provided to illustrate the syntax and structure of the package functions.
   • soil: soil physical data
   • weather: UWME weather data
   • papers: code used in the papers published by the author(s)
7. Graphics
   • Fitting a covariance function manuallyRFgui
   • the generic functionplot
   • global graphical parameters withRFpar
8. Coordinate systems
   • Cartesian, earth and spherical coordinates are recognized, seecoordinate systemsfor details.
   • a list of valid models is given byspherical models.
9. S3 and S4 objects
   • The functions return S4 objects based on the packagesp, ifspConform=TRUE. This is the default. IfspConform=FALSE, simple objects as in version 2 are returned. These simple objects are frequently provided with an S3 class. This options makes the returning procedure much faster, but currently does not allow for the comfortable use ofplot.
   • plot,print,summary, sometimes alsostrrecognise these S3 and S4 objects
   • usesp2RFfor an explicite transformation ofspobjects to S4 objects ofRandomFields.
   • Further generic functions are available for fitted models, seeInferenceabove. % \item \bold{Note} that, in many cases, \command{print} will return % an invisible list. This list contains the main information of the % S4 object in an accessible way and is in many cases the % information obtained from \code{summary}. See examples below.
10. Advancedusers, package programmers
    • might decide on a large variety of arguments of the simulation and estimation procedures using the functionRFoptions
    • may use./configure --with-tcl-config=/usr/lib/tcl8.5/tclConfig.sh --with-tk-config=/usr/lib/tk8.5/tkConfig.shto configure R

References

• Singleton, R.C. (1979). InPrograms for Digital Signal ProcessingEd.: Digital Signal Processing Committee and IEEE Acoustics, Speech, and Signal Processing Committe (1979) IEEE press.
• Schlather, M., Malinowski, A., Menck, P.J., Oesting, M. and Strokorb, K. (2015) Analysis, simulation and prediction of multivariate random fields with packageRandomFields.Journal of Statistical Software,63(8), 1-25, url =http://www.jstatsoft.org/v63/i08/
• see also the corresponding../doc/multivariate_jss.pdf{vignette}.

See Also

See also RF, RM, RP, RR, RC, R.

Examples

RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
##                   RFoptions(seed=NA) to make them all random again

# simulate some data first (Gaussian random field with exponential
# covariance; 6 realisations)
model <- RMexp()
x <- seq(0, 10, if (interactive()) 0.1 else 1)
z <- RFsimulate(model, x, x, n=6)

## select some data from the simulated data
xy <- as.matrix(expand.grid(x=x, y=x))
pts <- sample(nrow(xy), 100)
data <- matrix(ncol=6, as.vector(z))[pts, ]
data <- cbind(xy[pts, ], data)
plot(z, data)

## re-estimate the parameter (true values are 1)
estmodel <- RMexp(var=NA, scale=NA)
(fit <- RFfit(estmodel, data=data))

## show a kriged field based on the estimated parameters
kriged <- RFinterpolate(fit, x, x, data=data)
plot(kriged, data)

FinalizeExample()