make_Q_euler

The precision matrix for all vertices for space-time 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

make_Q_euler function

<dl><dt>graph</dt>
<dd>A <code>metric_graph</code> object.</dd>
<dt>t</dt>
<dd>Vector of time points.</dd>
<dt>kappa</dt>
<dd>Spatial range parameter.</dd>
<dt>rho</dt>
<dd>Drift parameter.</dd>
<dt>gamma</dt>
<dd>Temporal range parameter.</dd>
<dt>alpha</dt>
<dd>Smoothness parameter (integer) for spatial operator.</dd>
<dt>beta</dt>
<dd>Smoothness parameter (integer) for Q-Wiener process.</dd>
<dt>sigma</dt>
<dd>Variance parameter.</dd>
<dt>theta</dt>
<dd>Parameter theta for the Euler scheme.</dd></dl>

Arguments

Space-time precision operator Euler discretization — make_Q_euler

<dl>

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


<dt>t</dt>
<dd>Vector of time points.</dd>


<dt>kappa</dt>
<dd>Spatial range parameter.</dd>


<dt>rho</dt>
<dd>Drift parameter.</dd>


<dt>gamma</dt>
<dd>Temporal range parameter.</dd>


<dt>alpha</dt>
<dd>Smoothness parameter (integer) for spatial operator.</dd>


<dt>beta</dt>
<dd>Smoothness parameter (integer) for Q-Wiener process.</dd>


<dt>sigma</dt>
<dd>Variance parameter.</dd>


<dt>theta</dt>
<dd>Parameter theta for the Euler scheme.</dd>

</dl>

make_Q_euler: Space-time precision operator Euler discretization

Description

Usage

Value

Arguments