spde_precision

Computes the precision matrix for all vertices 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_precision function

<dl><dt>kappa</dt>
<dd>Range parameter.</dd>
<dt>tau</dt>
<dd>Precision parameter.</dd>
<dt>alpha</dt>
<dd>Smoothness parameter (1 or 2).</dd>
<dt>graph</dt>
<dd>A <code>metric_graph</code> object.</dd>
<dt>BC</dt>
<dd>Set boundary conditions for degree=1 vertices. BC =0 gives Neumann
boundary conditions and BC=1 gives stationary boundary conditions.</dd>
<dt>build</dt>
<dd>If <code>TRUE</code>, the precision matrix is returned. Otherwise a list
list(i,j,x, nv) is returned.</dd></dl>

Arguments

Precision matrix for Whittle-Matérn fields — spde_precision

<dl>

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


<dt>tau</dt>
<dd>Precision parameter.</dd>


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


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


<dt>BC</dt>
<dd>Set boundary conditions for degree=1 vertices. BC =0 gives Neumann
boundary conditions and BC=1 gives stationary boundary conditions.</dd>


<dt>build</dt>
<dd>If <code>TRUE</code>, the precision matrix is returned. Otherwise a list
list(i,j,x, nv) is returned.</dd>

</dl>

spde_precision: Precision matrix for Whittle-Matérn fields

Description

Usage

Value

Arguments