Abstract
FRK is an R software package for spatial/spatio-temporal modeling 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 modeling and prediction by avoiding stationary and isotropic covariance and variogram models, instead constructing a spatial random effects (SRE) model on a fine-resolution discretized 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-maximization (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 modeling.
Highlights
Fixed rank kriging (FRK) is a spatial/spatio-temporal modelling and prediction framework that is scaleable, works well with large datasets, and can deal with data that have different spatial supports
FRK hinges on the use of a spatial random effects (SRE) model, in which a spatially correlated mean-zero random process is decomposed using a linear combination of spatial basis functions with random coefficients plus a term that captures the random process’ fine-scale variation
We describe below the estimation procedure for the latter case; due to symmetry, the estimation equations of the former case can be obtained by replacing the subscript ξ with δ
Summary
Fixed rank kriging (FRK) is a spatial/spatio-temporal modelling and prediction framework that is scaleable, works well with large datasets, and can deal with data that have different spatial supports. Because the implied basis functions are constructed based on a parametric covariance model, a prior distribution on parameters results in new basis functions generated at each MCMC iteration Since this can slow down the computation, the number of knots used in predictive processes is usually chosen to be small, which has the effect of limiting their ability to model finer scales. In the standard ‘flavour’ of FRK (Cressie and Johannesson 2008), which we term vanilla FRK (FRK-V), there is an explicit reliance on multi-resolution basis functions to give complex nonstationary spatial patterns at the cost of not imposing any structure on K, the covariance matrix of the basis function weights This can result in identifiability issues and in Andrew Zammit-Mangion, Noel Cressie over-fitting the data when K is estimated using standard likelihood methods (e.g., Nguyen, Katzfuss, Cressie, and Braverman 2014), especially in regions of data paucity.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
