Mesh settings

Mesh Parameters

Parameters are on the scale of spatial coordinates (e.g., if working in Easting and Northing, the parameters will be in km).

max.edge defines the maximum length of triangle edges. Lower values mean smaller triangles, resulting in a finer overall mesh.
max.edge can have one or two input values.
- One value would be used for a mesh with no outer boundary extension (not recommended).
- Two values relate to the specification for the inner mesh (inside the inner mesh boundary) and outer mesh (between the inner and outer mesh boundaries).
In the outer mesh, max.edge can be very large, as we are not interested in fine-scale inference for this area. We also want this to be a large value to improve computational efficiency, as the number of nodes in the mesh is proportional to the running time of the model.
In the inner mesh, we need to have a fine enough resolution to capture the processes we are interested in. This means that we want the max.edge to be smaller than the spatial range across which we would expect our points to be correlated (SPDE range parameter).
- Initially, if we have no other prior knowledge about the SPDE range parameter, we can approximate it as 1/3 of the study area, but it should then be replaced once a posterior estimate is obtained. The max.edge should then be between 1/10 and 1/5 of this spatial range value.
A mesh with a finer resolution will lead to a higher number of mesh nodes, resulting in a model with a longer running time. So, when choosing a value for max.edge, consider the size of the study area and look at the number of nodes in your resulting mesh.

min.angle defines the minimum angles at which triangles join.
min.angle can have one or two input values.
- One value would be used for a mesh with no outer boundary extension (not recommended).
- Two values relate to the specification for the inner mesh (inside the inner mesh boundary) and outer mesh (between the inner and outer mesh boundaries).
I believe changing min.angle has a similar effect on the overall mesh to changing max.edge, but with a less intuitive interpretation. I would therefore avoid specifying this parameter explicitly in mesh construction.

offset defines the extension distance for the mesh boundaries.
offset can have one or two input values.
- One value would be used for a mesh with no outer boundary extension (not recommended).
- Two values relate to the specification for the inner mesh (inside the inner mesh boundary) and outer mesh (between the inner and outer mesh boundaries).
An outer boundary extension is required to buffer the Boundary Effect. The Boundary Effect is an increase in the SD of estimates near the boundary, due to a boundary condition imposed on the SPDE. In order to avoid this, we create a boundary extension, leaving this effect at the outer boundary, so it doesn’t impact our area of interest (within the inner boundary).
A general rule is to use 1\(\times\) the max.edge for the inner boundary offset and 5\(\times\) the max.edge for the outer boundary offset.
The effectiveness of our outer boundary on buffering the Boundary Effect can be evaluated using the meshbuilder() tool (example below).
If negative, offset is interpreted as a factor relative to the approximate data diameter.

cutoff defines the minimum allowed distance across which 2 mesh nodes are required. Nodes which are at most as far apart as this are replaced by a single vertex.
In other words, cutoff represents the minimum distance across which two vertices are required, and so works in tandem with max.edge to determine mesh resolution.
The main purpose of cutoff is to even-out the size of triangles in the mesh, so that all triangles in the area of interest (inside the inner mesh boundary) are a similar size.
- When using points as a base to build a mesh from, we can end up with clusters of small triangles around these points. Increasing cutoff smooths this out, so that all triangles in the inner mesh are a similar size. A cutoff value of max.edge/5 usually evens out clustering.
Decreasing the cutoff value can help to better represent complex boundaries such as coastlines, as the number of triangles along complex edges is increased. A larger cutoff value may smooth over these edges, resulting in a simplified representation of the boundary.

boundary can be used to include a polygon for the area of interest, and is used to create the inner mesh boundary.
There should be at least 1 ‘spatial range’ (i.e., posterior SPDE range parameter) between the boundary and any point. If this is not known, it can be initially approximated as 1/3 of the study area, but should then be replaced once a posterior estimate is obtained.

locs can be used to define point locations from which to build the initial triangulation nodes of the mesh.
This can result in clustering of mesh nodes around point locations, which if undesired, can be fixed using the cutoff parameter.

Important

This information is obtained from inlabru teaching materials documents Git Repo

For more information about mesh construction visit https://rpubs.com/jafet089/886687 ¹

This vignette was created based on the older inla.mesh.2d() function and will be updated to fmesher eventually.↩︎