RFMethods {RandomFields} | R Documentation |
PrintMethodList
prints the list of currently implemented methods for
simulating random fields
GetMethodNames
returns a list of currently implemented methods
PrintMethodList() GetMethodNames()
circulant embedding
. direct matrix decomposition
.add.MPP
(Random coins).Z(.) = sum_i m_i( . - x_i)
In this package, only stationary Poisson point fields
are allowed
as underlying unmarked point processes.
Thus, if the marks m_i
are all indicator functions, we obtain
a Poisson random field. If the intensity of the Poisson
process is high we obtain an approximate Gaussian random
field by the central limit theorem this is the
add.mpp
method.
max.MPP
(Boolean functions).max.mpp
method.
nugget
.spectral TBM
(Spectral turning bands).spectral TBM
does not differ from the other
turning bands methods. However, line simulations are performed by a
spectral technique (Mantoglou and Wilson, 1982); a
realisation is given as the cosine with random
amplitude and random phase.
The implementation allows the simulation of 2-dimensional random
fields defined on arbitrary points or arbitrary grids.
TBM2
, TBM3
(Turning bands methods).TBM2
) directly
in the 2-dimensional space.
Instead, 2-dimensional random fields are frequently obtained
by simulating a 3-dimensional random field (using
TBM3
) and taking a 2-dimensional cross-section.TBM2
and TBM3
allow for arbitrary points, and
arbitrary grids
(arbitrary number of points in each direction, arbitrary grid length
for each direction)
Most methods possess additional parameters,
see RFparameters()
that control the precision of the result. The default parameters
are chosen such that the simulations are fine for many models
and their parameters.
The example in EmpiricalVariogram()
shows a way of checking the precision.
Martin Schlather, Martin.Schlather@uni-bayreuth.de http://www.geo.uni-bayreuth.de/~martin
Gneiting, T. and Schlather, M. (2001) Statistical modeling with covariance functions. In preparation.
Schlather, M. (1999) An introduction to positive definite functions and to unconditional simulation of random fields. Technical report ST 99-10, Dept. of Maths and Statistics, Lancaster University.
Original work:
Chan, G. and Wood, A.T.A. (1997) An algorithm for simulating stationary Gaussian random fields. J. R. Stat. Soc., Ser. C 46, 171181.
Dietrich, C.R. and Newsam, G.N. (1993) A fast and exact method for multidimensional Gaussian stochastic simulations. Water Resour. Res. 29, 28612869.
Wood, A.T.A. and Chan, G. (1994) Simulation of stationary Gaussian processes in [0,1]^d J. Comput. Graph. Stat. 3, 409432.
Dietrich, C.R. (1995) A simple and efficient space domain implementation of the turning bands method. Water Resour. Res. 31, 147156.
Mantoglou, A. and Wilson, J.L. (1982) The turning bands method for simulation of random fields using line generation by a spectral method. Water. Resour. Res. 18, 13791394.
Matheron, G. (1973) The intrinsic random functions and their applications. Adv. Appl. Probab. 5, 439468.
Matheron, G. (1967) Elements pour une Theorie des Milieux Poreux. Paris: Masson.
GaussRF
, MaxStableRF
, and
RandomFields
.
PrintMethodList()