rspde.anistropic2d {rSPDE} | R Documentation |
Rational approximations of stationary anisotropic Gaussian Matern random fields
Description
rspde.anistropic2d
computes a Finite Element Method (FEM) approximation of a
Gaussian random field defined as the solution to the stochastic partial
differential equation (SPDE):
C(h) = \frac{\sigma^2}{2^{\nu-1}\Gamma(\nu)}(\sqrt{h^T H^{-1}h})^\nu K_\nu(\sqrt{h^T H^{-1}h})
, based on a SPDE representation of the form
(I - \nabla\cdot(H\nabla))^{(\nu+1)/2}u = c\sigma W
,
where $c>0$ is a constant. The matrix H
is defined as
\begin{bmatrix}
h_x^2 & h_xh_yh_{xy} \\
h_xh_yh_{xy} & h_y^2
\end{bmatrix}
Usage
rspde.anistropic2d(
mesh,
nu = NULL,
nu.upper.bound = 2,
rspde.order = 1,
prior.hx = NULL,
prior.hy = NULL,
prior.hxy = NULL,
prior.sigma = NULL,
prior.precision = NULL,
prior.nu = NULL,
prior.nu.dist = "lognormal",
nu.prec.inc = 0.01,
type.rational.approx = "brasil",
shared_lib = "detect",
debug = FALSE,
...
)
Arguments
mesh |
Spatial mesh for the FEM approximation. |
nu |
If nu is set to a parameter, nu will be kept fixed and will not
be estimated. If nu is |
nu.upper.bound |
Upper bound for the smoothness parameter |
rspde.order |
The order of the covariance-based rational SPDE approach. The default order is 1. |
prior.hx |
A list specifying the prior for the parameter |
prior.hy |
A list specifying the prior for the parameter |
prior.hxy |
A list specifying the prior for the parameter |
prior.sigma |
A list specifying the prior for the variance parameter |
prior.precision |
A precision matrix for |
prior.nu |
a list containing the elements |
prior.nu.dist |
The distribution of the smoothness parameter. The current options are "beta" or "lognormal". The default is "lognormal". |
nu.prec.inc |
Amount to increase the precision in the beta prior distribution. Check details below. |
type.rational.approx |
Which type of rational approximation should be used? The current types are "brasil", "chebfun" or "chebfunLB". |
shared_lib |
String specifying which shared library to use for the Cgeneric implementation. Options are "detect", "INLA", or "rSPDE". You may also specify the direct path to a .so (or .dll) file. |
debug |
Logical value indicating whether to enable INLA debug mode. |
... |
Additional arguments passed internally for configuration purposes. |
Value
An object of class inla_rspde_spacetime
representing the FEM approximation of
the space-time Gaussian random field.