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
$$\begin{bmatrix}
h_x^2 & h_xh_yh_{xy} \\
h_xh_yh_{xy} & h_y^2
\end{bmatrix}$$
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,
...
)An object of class inla_rspde_spacetime representing the FEM approximation of
the space-time Gaussian random field.
Spatial mesh for the FEM approximation.
If nu is set to a parameter, nu will be kept fixed and will not
be estimated. If nu is NULL, it will be estimated.
Upper bound for the smoothness parameter \(\nu\). If NULL, it will be set to 2.
The order of the covariance-based rational SPDE approach. The default order is 1.
A list specifying the prior for the parameter \(h_x\) in the matrix \(H\). This list may contain two elements: mean and/or precision, both of which must be numeric scalars. The precision refers to the prior on \(\log(h_x)\). If NULL, default values will be used. The mean value is also used as starting value for hx.
A list specifying the prior for the parameter \(h_y\) in the matrix \(H\). This list may contain two elements: mean and/or precision, both of which must be numeric scalars. The precision refers to the prior on \(\log(h_x)\). If NULL, default values will be used. The mean value is also used as starting value for hy.
A list specifying the prior for the parameter \(h_x\) in the matrix \(H\). This list may contain two elements: mean and/or precision, both of which must be numeric scalars. The precision refers to the prior on \(\log((h_{xy}+1)/(1-h_{xy}))\). If NULL, default values will be used. The mean value is also used as starting value for hxy.
A list specifying the prior for the variance parameter \(\sigma\).
This list may contain two elements: mean and/or precision, both of which must
be numeric scalars. The precision refers to the prior on \(\log(\sigma)\). If NULL,
default values will be used. The mean value is also used as starting value for sigma.
A precision matrix for \(\log(h_x), \log(h_y), \log((h_{xy}+1)/(1-h_{xy})), \log(\sigma)\). This matrix replaces the precision
element from prior.kappa, prior.sigma, prior.gamma, and prior.rho respectively. For dimension 1 prior.precision must be a 4x4 matrix. For dimension 2, \(\rho\) is a vector of length 2, so in this case prior.precision must be a 5x5 matrix. If NULL, a diagonal precision matrix with default values will be used.
a list containing the elements mean and prec
for beta distribution, or loglocation and logscale for a
truncated lognormal distribution. loglocation stands for
the location parameter of the truncated lognormal distribution in the log
scale. prec stands for the precision of a beta distribution.
logscale stands for the scale of the truncated lognormal
distribution on the log scale. Check details below.
The distribution of the smoothness parameter. The current options are "beta" or "lognormal". The default is "lognormal".
Amount to increase the precision in the beta prior distribution. Check details below.
Which type of rational approximation should be used? The current types are "brasil", "chebfun" or "chebfunLB".
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.
Logical value indicating whether to enable INLA debug mode.
Additional arguments passed internally for configuration purposes.