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]