Description Usage Arguments Details Value References Examples
Simulate stationary and isotropic 2D Mat\'ern Gaussian random field using Markov approximation in a grid. Also conditional with given data.
1 2 3 4 5 6 |
ncol, nrow |
Grid dimensions. ncol in x direction. |
xlim, ylim |
Spatial dimensions, rectangular window. |
expand |
Expansion of the grid for border bias elimination. If not given, computed using |
tau |
Precision i.e. inverse variance. |
range |
Range of covariance, controls smoothness. |
nu |
The differentiability parameter of covariance. Accepts: 1,2,3. |
cyclic |
Use cyclic (toroidal) grid. |
dbg |
Verbose output during simulation. |
use.RandomFields |
Option to use randomFields package for conditional simulation. |
... |
If using randomFields, these are passed on to the CondSimu-function. |
data |
List with components x,y and v giving the x- and y-coordinates of values v for conditional simulation. |
The stationary and isotropic Mat\'ern covariance function at distance t is
C(t) \propto tau*(kappa*t)^nu K_{nu}(kappa*t)
where tau is the precision (inverse variance), nu is differentiability of the covariance, and kappa is the scale. We use a transformed kappa called range r=sqrt(8*nu)/kappa so that C(r)~=0.1.
The simulation is done using Markov approximation, see Held \& Rue 2005 and Lindgren et al 2011. Hence the term GMRF: Gaussian Markov Random Field.
Object of class rfhcField
which is the same as object of class im
with the simulation parameters
stored in the element $parameters.
Held, Rue (2005) Gaussian Markov Random Fields: Theory and Applications. Chapman&Hall/CRC.
Lindgren, Rue, Lindst\"om (2011) An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach J. R. Statistic. Soc. B. 73.
1 2 | y<-simulateGMRF()
plot(y)
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