A geostatistical framework for heterogeneous spatial data fusion

This paper proposes a geostatistical framework of spatial data fusion for spatial prediction and uncertainty modeling, while accounting for varieties of spatial heterogeneities and complex spatial dependencies. Within this proposed framework, spatial variables are characterized via spatial covariance functions, which measure the spatial dependencies of pair-wise locations and project heterogeneous spatial data into a unified space of similarity (or kernel space). The representation of spatial covariance thus provides a convenient venue to integrate heterogeneous data source while taking into account spatial dependencies. We show that the probability distribution at target locations given the neighboring observations can be represented as a generalized linear combination of spatial covariance functions between the target and observed locations. For parameter estimation, a recently proposed group LASSO (Least Absolute Shrinkage and Selection Operator)) approach is adopted to prevent the model from over-fitting. Case studies are conducted to showcase the advantages of the proposed framework.