spde_covariance

Computes the covariance function for a Whittle-Matérn field.

Facilitates creation and manipulation of metric graphs, such as street or river networks. Further facilitates operations and visualizations of data on metric graphs, and the creation of a large class of random fields and stochastic partial differential equations on such spaces. These random fields can be used for simulation, prediction and inference. In particular, linear mixed effects models including random field components can be fitted to data based on computationally efficient sparse matrix representations. Interfaces to the R packages 'INLA' and 'inlabru' are also provided, which facilitate working with Bayesian statistical models on metric graphs. The main references for the methods are Bolin, Simas and Wallin (2024) <doi:10.3150/23-BEJ1647>, Bolin, Kovacs, Kumar and Simas (2023) <doi:10.1090/mcom/3929> and Bolin, Simas and Wallin (2023) <doi:10.48550/arXiv.2304.03190> and <doi:10.48550/arXiv.2304.10372>.

David Bolin

MetricGraph

Random Fields on Metric Graphs

Alexandre Simas

Jonas Wallin

spde_covariance function

<dl><dt>P</dt>
<dd>Location (edge number and normalized location on the edge) for the
location to evaluate the covariance function at.</dd>
<dt>kappa</dt>
<dd>Parameter kappa from the SPDE.</dd>
<dt>tau</dt>
<dd>Parameter tau from the SPDE.</dd>
<dt>range</dt>
<dd>Range parameter.</dd>
<dt>sigma</dt>
<dd>Standard deviation parameter.</dd>
<dt>alpha</dt>
<dd>Smoothness parameter (1 or 2).</dd>
<dt>graph</dt>
<dd>A <code>metric_graph</code> object.</dd>
<dt>directional</dt>
<dd>bool is the model a directional or not. directional only works for alpha=1</dd></dl>

Arguments

Covariance function for Whittle-Matérn fields — spde_covariance

<dl>

<dt>P</dt>
<dd>Location (edge number and normalized location on the edge) for the
location to evaluate the covariance function at.</dd>


<dt>kappa</dt>
<dd>Parameter kappa from the SPDE.</dd>


<dt>tau</dt>
<dd>Parameter tau from the SPDE.</dd>


<dt>range</dt>
<dd>Range parameter.</dd>


<dt>sigma</dt>
<dd>Standard deviation parameter.</dd>


<dt>alpha</dt>
<dd>Smoothness parameter (1 or 2).</dd>


<dt>graph</dt>
<dd>A <code>metric_graph</code> object.</dd>


<dt>directional</dt>
<dd>bool is the model a directional or not. directional only works for alpha=1</dd>

</dl>

spde_covariance: Covariance function for Whittle-Matérn fields

Description

Usage

Value

Arguments

Details