`rSPDE`

is used for approximating fractional elliptic SPDEs
$$L^\beta (\tau u(s)) = W,$$
where \(L\) is a differential operator and \(\beta>0\)
is a general fractional power.

## Details

The approximation is based on a rational approximation of the fractional operator, and allows for computationally efficient inference and simulation.

The main functions for computing rational approximation objects are:

`fractional.operators()`

works for general rational operators

`matern.operators()`

works for random fields with stationary Matern covariance functions

`spde.matern.operators()`

works for random fields with defined as solutions to a possibly non-stationary Matern-type SPDE model.

`rspde.matern()`

R-INLA implementation of the covariance-based rational approximation for random fields with stationary Matern covariance functions

Basic statistical operations such as likelihood evaluations (see
`[rSPDE.loglike], [rSPDE.matern.loglike]`

) and kriging
predictions (see `[predict.rSPDEobj], [predict.CBrSPDEobj]`

)
using the rational approximations are also implemented.

For illustration purposes, the package contains a simple FEM implementation
for models on R. For spatial models,
the FEM implementation in the `R-INLA`

package is recommended.

For a more detailed introduction to the package, see the rSPDE Vignettes.

## Author

**Maintainer**: David Bolin davidbolin@gmail.com

Authors:

Alexandre Simas alexandre.impa@gmail.com

Other contributors:

Finn Lindgren finn.lindgren@ed.ac.uk [contributor]