Kernel-Based Sparse Bayesian Learning for Interpolating Spatial Data

Interpolation of spatial variables is of primary importance for hydrogeological applications. Various approaches have been considered in geostatistical literature to address this issue. However, most traditional interpolation methods, including inverse distance weighting, standard kriging and radial basis functions techniques have various limitations. Kernel-based sparse bayesian learning, which has received much attention in the context of regression and classification, can provide a probabilistic framework for spatial interpolation. This study reports the use of the theory of relevance vector machine (RVM), a particular specialization of bayesian learning, for interpolating spatial variables at unknown locations. An important practical question dealing with the selection of the kernel function parameters in the design of RVMs is addressed here. The results indicate that the proposed method of selecting kernel parameters can translate into improved performance of RVMs.