Matern rSPDE model object for INLA — rspde.matern • rSPDE

Creates an INLA object for a stationary Matern model with general smoothness parameter.

Usage

rspde.matern(
  mesh,
  nu.upper.bound = NULL,
  rspde.order = 1,
  nu = NULL,
  B.sigma = matrix(c(0, 1, 0), 1, 3),
  B.range = matrix(c(0, 0, 1), 1, 3),
  parameterization = c("spde", "matern", "matern2"),
  B.tau = matrix(c(0, 1, 0), 1, 3),
  B.kappa = matrix(c(0, 0, 1), 1, 3),
  start.nu = NULL,
  start.theta = NULL,
  prior.nu = NULL,
  theta.prior.mean = NULL,
  theta.prior.prec = 0.1,
  prior.std.dev.nominal = 1,
  prior.range.nominal = NULL,
  prior.kappa.mean = NULL,
  prior.tau.mean = NULL,
  start.lstd.dev = NULL,
  start.lrange = NULL,
  start.ltau = NULL,
  start.lkappa = NULL,
  prior.theta.param = c("theta", "spde"),
  prior.nu.dist = c("beta", "lognormal"),
  nu.prec.inc = 1,
  type.rational.approx = c("brasil", "chebfun", "chebfunLB"),
  debug = FALSE,
  shared_lib = "detect",
  ...
)

Arguments

mesh: The mesh to build the model. It can be an inla.mesh or an inla.mesh.1d object. Otherwise, should be a list containing elements d, the dimension, C, the mass matrix, and G, the stiffness matrix.
nu.upper.bound: Upper bound for the smoothness parameter. If NULL, it will be set to 2.
rspde.order: The order of the covariance-based rational SPDE approach. The default order is 1.
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.
B.sigma: Matrix with specification of log-linear model for \(\sigma\) (for 'matern' parameterization) or for \(\sigma^2\) (for 'matern2' parameterization). Will be used if parameterization = 'matern' or parameterization = 'matern2'.
B.range: Matrix with specification of log-linear model for \(\rho\), which is a range-like parameter (it is exactly the range parameter in the stationary case). Will be used if parameterization = 'matern' or parameterization = 'matern2'.
parameterization: Which parameterization to use? matern uses range, std. deviation and nu (smoothness). spde uses kappa, tau and nu (smoothness). matern2 uses range-like (1/kappa), variance and nu (smoothness). The default is spde.
B.tau: Matrix with specification of log-linear model for \(\tau\). Will be used if parameterization = 'spde'.
B.kappa: Matrix with specification of log-linear model for \(\kappa\). Will be used if parameterization = 'spde'.
start.nu: Starting value for nu.
start.theta: Starting values for the model parameters. In the stationary case, if parameterization='matern', then theta[1] is the std.dev and theta[2] is the range parameter. If parameterization = 'spde', then theta[1] is tau and theta[2] is kappa.
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.
theta.prior.mean: A vector for the mean priors of theta.
theta.prior.prec: A precision matrix for the prior of theta.
prior.std.dev.nominal: Prior std. deviation to be used for the priors and for the starting values.
prior.range.nominal: Prior range to be used for the priors and for the starting values.
prior.kappa.mean: Prior kappa to be used for the priors and for the starting values.
prior.tau.mean: Prior tau to be used for the priors and for the starting values.
start.lstd.dev: Starting value for log of std. deviation. Will not be used if start.ltau is non-null. Will be only used in the stationary case and if parameterization = 'matern'.
start.lrange: Starting value for log of range. Will not be used if start.lkappa is non-null. Will be only used in the stationary case and if parameterization = 'matern'.
start.ltau: Starting value for log of tau. Will be only used in the stationary case and if parameterization = 'spde'.
start.lkappa: Starting value for log of kappa. Will be only used in the stationary case and if parameterization = 'spde'.
prior.theta.param: Should the lognormal prior be on theta or on the SPDE parameters (tau and kappa on the stationary case)?
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".
debug: INLA debug argument
shared_lib: Which shared lib to use for the cgeneric implementation? "detect" and "INLA" prefer the model compiled into the INLA binary and fall back to a compiled local rSPDE library when the symbol is unavailable. "rSPDE" requires the local library. An existing .so or .dll path can also be supplied directly.
...: Only being used internally.
prior.kappa: a list containing the elements meanlog and sdlog, that is, the mean and standard deviation on the log scale.
prior.tau: a list containing the elements meanlog and sdlog, that is, the mean and standard deviation on the log scale.
prior.range: a list containing the elements meanlog and sdlog, that is, the mean and standard deviation on the log scale. Will not be used if prior.kappa is non-null.
prior.std.dev: a list containing the elements meanlog and sdlog, that is, the mean and standard deviation on the log scale. Will not be used if prior.tau is non-null.

Value

An INLA model.