sample_spde: Samples a Whittle-Matérn field on a metric graph

Description

Obtains samples of a Whittle-Matérn field on a metric graph.

Usage

sample_spde(
  kappa,
  tau,
  range,
  sigma,
  sigma_e = 0,
  alpha = 1,
  directional = FALSE,
  graph,
  PtE = NULL,
  type = "manual",
  posterior = FALSE,
  nsim = 1,
  method = c("conditional", "Q"),
  BC = 1
)

Value

Matrix or vector with the samples.

Arguments

kappa: Range parameter.
tau: Precision parameter.
range: Practical correlation range parameter.
sigma: Marginal standard deviation parameter.
sigma_e: Standard deviation of the measurement noise.
alpha: Smoothness parameter.
directional: should we use directional model currently only for alpha=1
graph: A metric_graph object.
PtE: Matrix with locations (edge, normalized distance on edge) where the samples should be generated.
type: If "manual" is set, then sampling is done at the locations specified in PtE. Set to "mesh" for simulation at mesh nodes, and to "obs" for simulation at observation locations.
posterior: Sample conditionally on the observations?
nsim: Number of samples to be generated.
method: Which method to use for the sampling? The options are "conditional" and "Q". Here, "Q" is more stable but takes longer.
BC: Boundary conditions for degree 1 vertices. BC = 0 gives Neumann boundary conditions and BC = 1 gives stationary boundary conditions.

Details

Samples a Gaussian Whittle-Matérn field on a metric graph, either from the prior or conditionally on observations $$y_i = u(t_i) + \sigma_e e_i$$ on the graph, where $e_i$ are independent standard Gaussian variables. The parameters for the field can either be specified in terms of tau and kappa or practical correlation range and marginal standard deviation.