Matern correlation or covariance function approximate credible bands.

Evaluate the covariance function for an inla.spde object. Calculates the posterior distribution of the range, log(range), variance, or log(variance) parameter of a model's SPDE component. Can also calculate Matern correlation or covariance function.

Usage

materncov.bands(
  manifold,
  dist,
  log.range,
  log.variance = NULL,
  alpha = 2,
  quantile = 0.95,
  n = 64,
  S1.L = NULL
)

Arguments

manifold: Either "R1", "S1", "R2", or "S2", from fm_manifold(mesh), or a full fm_mesh_2d or fm_mesh_1d object.
dist: A vector of distances at which to calculate the covariances/correlations
log.range: A scalar or a list (mean, sd), such as produced by inla.spde.result(...)$summary.log.range.nominal[[1]][c("mean","sd")]
log.variance: Either NULL, a scalar, or vector of the same type as for log.range. When NULL, the correlations are calculated instead of the covariances.
alpha: The SPDE operator order. Default 2.
quantile: The target credible probability. Default 0.95.
n: The number of parameter combinations to use for the approximation. Default 64.
S1.L: For manifold "S1", give the length of the cyclic interval

Value

A list with estimated covariance or correlation (when log.variance is NULL) functions:

lower: An approximate lower bound for the quantile credible region
median: The function for for the approximate median parameters quantile
upper: An approximate upper bound for the quantile credible region

Details

Uses a Gaussian assumption for the internal model parameters, and finds a region in parameter space with approximately quantile probability.

Author

Finn Lindgren Finn.Lindgren@ed.ac.uk