Simulation and Analysis of Random Fields
Description
The package RandomFields
offers various tools for
model estimation (ML) and inference (tests) for regionalized variables and data analysis,
simulation of different kinds of random fields, including
multivariate, spatial, spatiotemporal, and nonstationary Gaussian random fields,
Poisson fields, binary fields, Chi2 fields, t fields and
maxstable fields.
It can also deal with nonstationarity and anisotropy of these processes and conditional simulation (for Gaussian random fields, currently).
See http://ms.math.unimannheim.de/de/publications/software/ for intermediate updates.
Details
The following features are provided by the package:

Bayesian Modelling
See Bayesian Modelling for an introduction to hierarchical modelling

Coordinate systems
Cartesian, earth and spherical coordinates are recognized, see coordinate systems for details.
a list of valid models is given by spherical models.

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)


Estimation of parameters (for secondorder 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


Graphics
Fitting a covariance function manually
RFgui
the generic function
plot
global graphical parameters with
RFpar

Inference (for Gaussian random fields)

RFcrossvalidate
: cross validation 
RFlikelihood
: likelihood 
RFratiotest
: likelihood ratio test 
AIC
,AICc
,BIC
,anova
,logLik


Models
For an introduction an general properties, see RMmodels.
For an overview over classes of covariance and variogram models –e.g. for geostatistical purposes– see RM. More sophisticated models and covariance function operators are included.
To apply the offered package procedures to mixed models – e.g. appearing in genetical data analysis– see
RFformula
.definite models are evaluated by
RFcov
,RFvariogram
andRFcovmatrix
. For a quick impression useplot(model)
.nondefinte models are evaluated by
RFfctn
andRFcalc

RFlinearpart
returns the linear part of a model 
RFboxcox
deals explicitely with BoxCox transformations. In many cases it is performed implicitely.

Prediction (for secondorder random fields)

RFinterpolate
: kriging, including imputing


Simulation

RFsimulate
: Simulation of random fields, including conditional simulation. For a list of all covariance functions and variogram models seeRM
. Useplot
for visualisation of the result.


S3 and S4 objects
The functions return S4 objects based on the package sp, if
spConform=TRUE
. This is the default.If
spConform=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 alsostr
recognise these S3 and S4 objects use
sp2RF
for an explicite transformation of sp objects to S4 objects of RandomFields.
Further generic functions are available for fitted models, see ‘Inference’ above.

Xtended features, especially for package programmers
might decide on a large variety of arguments of the simulation and estimation procedures using the function
RFoptions
may use ‘./configure –withtclconfig=/usr/lib/tcl8.5/tclConfig.sh –withtkconfig=/usr/lib/tk8.5/tkConfig.sh’ to configure R
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.unimannheim.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, 201112)
Sebastian Gross (Univ. Goettingen; tilde formulae, 2011)
Alexander Malinowski (Univ. Mannheim; S3, S4 classes 201113)
Juliane Manitz (Univ. Goettingen; testing, 2012)
Johannes Martini (Univ. Goettingen; RFempiricalvariogram, 201112)
Ulrike Ober (Univ. Goettingen; help pages, testing, 201112)
Marco Oesting (Univ. Mannheim; BrownResnick processes, Kriging, Trend, 201113)
Paulo Ribeiro (Unversidade Federal do Parana; code adopted from geoR, 2014)
Kirstin Strokorb (Univ. Mannheim; help pages, 201113)
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 1953 ‘Statistical Modeling of Complex Systems and Processes — Advanced Nonparametric Approaches’ (20132018).

V3.0 has been financially supported by Volkswagen Stiftung within the project ‘WEXMOP’ (20112014).

Alpha versions for V3.0 have been financially supported by the German Science Foundation (DFG) through the Research Training Groups 1644 ‘Scaling problems in Statistics’ and 1023 ‘Identification in Mathematical Models’ (200813).

V1.0 has been financially supported by the German Federal Ministry of Research and Technology (BMFT) grant PT BEO 510339476C during 200003.

V1.0 has been financially supported by the EU TMR network ERBFMRXCT960095 on “Computational and statistical methods for the analysis of spatial data” in 1999.
Note
The following packages enable further choices for the optimizer
(instead of optim
) in RandomFields:
optimx, soma, GenSA, minqa, pso,
DEoptim, nloptr, RColorBrewer, colorspace
Author(s)
Martin Schlather, schlather@math.unimannheim.de http://ms.math.unimannheim.de/de/publications/software
References

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.

Schlather, M., Malinowski, A., Menck, P.J., Oesting, M. and Strokorb, K. (2015) Analysis, simulation and prediction of multivariate random fields with package RandomFields. Journal of Statistical Software, 63 (8), 125, url = ‘http://www.jstatsoft.org/v63/i08/’

see also the corresponding vignette.
See Also
See also RF, RM, RP, RR, RC, R.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23  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, 0.1)
z < RFsimulate(model, x, x, n=6)
## select some data from the simulated data
xy < coordinates(z)
pts < sample(nrow(xy), min(100, nrow(xy) / 2))
data < matrix(nrow=nrow(xy), as.vector(z))[pts, ]
data < cbind(xy[pts, ], data)
plot(z, data)
## reestimate 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)
