Description
Fixed Rank Kriging is a tool for spatial/spatio-temporal modelling and prediction with large datasets. The approach models the field, and hence the covariance function, using a set of r basis functions, where r is typically much smaller than the number of data points (or polygons) m. This low-rank basis-function representation facilitates the modelling of 'big' spatial/spatio-temporal data. The method naturally allows for non-stationary, anisotropic covariance functions. Discretisation of the spatial domain into so-called basic areal units (BAUs) facilitates the use of observations with varying support (i.e., both point-referenced and areal supports, potentially simultaneously), and prediction over arbitrary user-specified regions. `FRK` also supports inference over various manifolds, including the 2D plane and 3D sphere, and it provides helper functions to model, fit, predict, and plot with relative ease. Version 2.0.0 and above of the package `FRK` also supports modelling of non-Gaussian data, by employing a spatial generalised linear mixed model (GLMM) framework to cater for Poisson, binomial, negative-binomial, gamma, and inverse-Gaussian distributions. Zammit-Mangion and Cressie describe `FRK` in a Gaussian setting, and detail its use of basis functions and BAUs.