Finn Lindgren

Eliminating the practical boundary between Markov and
other Gaussian random fields


Abstract:

Gaussian random field models are used extensively in spatial and
spatio-temporal statistics.  Traditionally, two largely separate
approaches have been used; covariance function specifications and
grid-based Markov random fields.  The former method is appealing in
its directness, but computationally costly, whereas the latter is
appealing for its computational benefits.  The two approaches have
coexisted without much direct links between the specifications.

In this seminar I will explain how to construct a direct specification
of Markov random fields approximating the MatŽrn family of covariance
models, through stochastic partial differential equations.  As a
simple side-effect, this model class can be expanded to fields on
curved surfaces, such as a globe, as well as non-trivially anisotropic
and oscillating fields, illustrated with geo-statistical data.  The
approach also provides a link to other random field models, such as
convolution fields and spectral representations