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

In MetricGraph: Random Fields on Metric Graphs

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
)

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.

Value

Matrix or vector with the samples.

MetricGraph documentation built on April 3, 2025, 10:34 p.m.