  FRK is an R software package for spatial/spatio-temporal modelling and
prediction with large datasets. It facilitates optimal spatial prediction
(kriging) on the most commonly used manifolds (in Euclidean space and on the
surface of the sphere), for both spatial and spatio-temporal fields. It differs
from many of the packages for spatial modelling and prediction by avoiding
stationary and isotropic covariance and variogram models, instead constructing
a spatial random effects (SRE) model on a fine-resolution discretised spatial
domain. The discrete element is known as a basic areal unit (BAU), whose
introduction in the software leads to several practical advantages. The
software can be used to (i) integrate multiple observations with different
supports with relative ease; (ii) obtain exact predictions at millions of
prediction locations (without conditional simulation); and (iii) distinguish
between measurement error and fine-scale variation at the resolution of the
BAU, thereby allowing for reliable uncertainty quantification. The temporal
component is included by adding another dimension. A key component of the SRE
model is the specification of spatial or spatio-temporal basis functions; in
the package, they can be generated automatically or by the user. The package
also offers automatic BAU construction, an expectation-maximisation (EM)
algorithm for parameter estimation, and functionality for prediction over any
user-specified polygons or BAUs. Use of the package is illustrated on several
spatial and spatio-temporal datasets, and its predictions and the model it
implements are extensively compared to others commonly used for spatial
prediction and modelling.
