ABSTRACT
This chapter introduces a general prediction formula for all spatial interpolation methods in this book firstly, then introduces mathematical spatial interpolation methods. These methods are deterministic and non-geostatistical spatial interpolation methods, which are based only on the mathematical calculations of spatial information (i.e., coordinates data) and do not involve spatial changes of data variances. In this chapter, the mathematical methods that are available in R are introduced, including: 1) inverse distance weighted (IDW); 2) nearest neighbours (NN); and 3) k nearest neighbours (KNN). The chapter also demonstrates how to use the function idwcv in the spm package for estimating the optimal parameters that can maximize the predictive accuracy of IDW, NN and KNN; and the function idwpred in the spm package for generating the spatial predictions of these methods. The swmud point data and sw grid data in the spm package are used to demonstrate the applications of these methods.
