graph_spde {MetricGraph}

'INLA' implementation of Whittle-Matérn fields for metric graphs

Description

This function creates an 'INLA' object that can be used in 'INLA' or 'inlabru' to fit Whittle-Matérn fields on metric graphs.

Usage

graph_spde(
  graph_object,
  alpha = 1,
  stationary_endpoints = "all",
  parameterization = c("matern", "spde"),
  start_range = NULL,
  prior_range = NULL,
  start_kappa = NULL,
  start_sigma = NULL,
  prior_kappa = NULL,
  prior_sigma = NULL,
  shared_lib = "detect",
  debug = FALSE
)

Arguments

graph_object

A metric_graph object.

alpha

The order of the SPDE.

stationary_endpoints

Which vertices of degree 1 should contain stationary boundary conditions?

parameterization

Which parameterization to be used? The options are 'matern' (sigma and range) and 'spde' (sigma and kappa).

start_range

Starting value for range parameter.

prior_range

a list containing the elements meanlog and sdlog, that is, the mean and standard deviation of the range parameter on the log scale. Will not be used if prior.kappa is non-null.

start_kappa

Starting value for kappa.

start_sigma

Starting value for sigma.

prior_kappa

a list containing the elements meanlog and sdlog, that is, the mean and standard deviation of kappa on the log scale.

prior_sigma

a list containing the elements meanlog and sdlog, that is, the mean and standard deviation of sigma on the log scale.

shared_lib

Which shared lib to use for the cgeneric implementation? If "detect", it will check if the shared lib exists locally, in which case it will use it. Otherwise it will use 'INLA's shared library. If 'INLA', it will use the shared lib from 'INLA's installation. If 'MetricGraph', then it will use the local installation (does not work if your installation is from CRAN). Otherwise, you can directly supply the path of the .so (or .dll) file.

debug

Should debug be displayed?

Details

This function is used to construct a Matern SPDE model on a metric graph. The latent field u is the solution of the SPDE

(\kappa^2 - \Delta)^\alpha u = \sigma W,

where W is Gaussian white noise on the metric graph. This model implements exactly the cases in which \alpha = 1 or \alpha = 2. For a finite element approximation for general \alpha we refer the reader to the 'rSPDE' package and to the Whittle–Matérn fields with general smoothness vignette.

We also have the alternative parameterization \rho = \frac{\sqrt{8(\alpha-0.5)}}{\kappa}, which can be interpreted as a range parameter.

Let \kappa_0 and \sigma_0 be the starting values for \kappa and \sigma, we write \sigma = \exp\{\theta_1\} and \kappa = \exp\{\theta_2\}. We assume priors on \theta_1 and \theta_2 to be normally distributed with mean, respectively, \log(\sigma_0) and \log(\kappa_0), and variance 10. Similarly, if we let \rho_0 be the starting value for \rho, then we write \rho = \exp\{\theta_2\} and assume a normal prior for \theta_2, with mean \log(\rho_0) and variance 10.

Value

An 'INLA' object.