simulateGMRF: Simulate 2D Mat\'ern Field Using Markov Approximation.
In antiphon/rfhc: Random field + Hardcore Gibbs model

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.

simulateGMRF(ncol=50, nrow=50, tau=3, range=0.3, nu=2, expand,
             xlim=c(0,1), ylim=c(0,1), cyclic=FALSE, dbg=0)
simulate_condGMRF(ncol=50, nrow=50, tau=5, range=0.2, nu=2, 
                  expand, xlim=c(0,1), ylim=c(0,1), 
                  data=list(x=.5, y=.5, v=0), 
                  cyclic=FALSE, dbg=0, use.RandomFields=FALSE, ...)

`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 `nu`.
`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.