sample_spde {MetricGraph}

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,
  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.

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.