Rational approximations of fractional intrinsic fields

rspde.intrinsic computes a Finite Element Method (FEM) approximation of a Gaussian random field defined as the solution to the stochastic partial differential equation (SPDE): $$(-\Delta)^{(\nu+d/2)/2}\tau u = W$$.

Usage

rspde.intrinsic(
  mesh,
  nu = NULL,
  nu.upper.bound = 2,
  mean.correction = FALSE,
  rspde.order = 1,
  prior.tau = NULL,
  prior.nu = NULL,
  prior.nu.dist = "lognormal",
  nu.prec.inc = 0.01,
  diagonal = 0,
  type.rational.approx = "chebfun",
  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 NULL, it will be estimated.
nu.upper.bound: Upper bound for the smoothness parameter $\nu$. If NULL, it will be set to 2.
mean.correction: Add mean correction for extreme value models?
rspde.order: The order of the covariance-based rational SPDE approach. The default order is 1.
prior.tau: A list specifying the prior for the variance parameter $\tau$. This list may contain two elements: mean and/or precision, both of which must be numeric scalars.
prior.nu: 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.
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.
diagonal: Number added to diagonal of Q for increased stability.
type.rational.approx: Which type of rational approximation should be used? The current types are "chebfun", "brasil" 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_intrinsic representing the FEM approximation of the intrinsic Gaussian random field.

Examples

library(fmesher)
n_loc <- 2000
loc_2d_mesh <- matrix(runif(n_loc * 2), n_loc, 2)
mesh_2d <- fm_mesh_2d(loc = loc_2d_mesh, cutoff = 0.03, max.edge = c(0.1, 0.5))
model <- rspde.intrinsic(mesh = mesh_2d)