Explicit construction of GMRF approximations to generalised Matérn
fields on irregular grids
Finn Lindgren and Håvard Rue
Centre for Mathematical Sciences
Lund Institute of Technology,
Models based on stationary covariance functions, such as the Matérn
family, are commonly used in spatial statistics. For large grid resolutions,
the computational effort can be substantial, as well as the memory requirements.
A solution to this problem is to approximate the stationary covariances with
a Markov random field model on the grid. This report contains the theoretical
basis for one such approximation method, using the finite element method
to explicitly construct sparse precision matrices for the solutions to the
same stochastic partial differential equations that generate the Matérn
covariances. The method can be applied not only for planar regular grids,
but also on irregular triangulations of curved manifolds.