Before revision:  Existing methods for spatial interpolation, most notably Gaussian processes and spatial autoregressive models, tend to suffer from  (a) a trade-off between modelling local or global spatial interaction , (b) the assumption there is only one possible path between two points , and (c) the assumption of homogeneity of intermediate locations between points .
After revision:  Existing methods for spatial interpolation, most notably Gaussian processes and spatial autoregressive models, tend to suffer from (a) a trade-off between modelling local or global spatial interaction , (b) the assumption of isotropy , and (c) the assumption of homogeneity of intermediate locations between points .