rSPDE: Rational approximations of fractional SPDEs.

In rSPDE: Rational Approximations of Fractional Stochastic Partial Differential Equations

Rational approximations of fractional SPDEs.

Description

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.

rSPDE documentation built on Nov. 6, 2023, 1:06 a.m.