Abstract: We develop a multiscale spatial kernel convolution technique that employs higher-order functions to capture fine-scale local features, and lower-order terms to capture large-scale features. To achieve parsimony, the coefficients in the proposed model are assigned a new class of "tree shrinkage prior" distributions. Tree shrinkage priors exert increasing shrinkage on the coefficients as the resolution increases, enabling them to adapt to the necessary degree of resolution at any sub-domain. In contrast to existing multiscale approaches, our approach auto-tunes the degree of resolution necessary to model a subregion in the domain, and achieves scalability by parallelizing the local updating of the parameters. The empirical performance of the proposed method is illustrated using several simulation experiments and a geostatistical analysis of sea surface temperature data from the Pacific Ocean.

Key words and phrases: Discrete kernel convolution, large spatial data, multiscale modeling, sea surface temperature, tree shrinkage prior.