  We develop a multiscale spatial kernel convolution technique with 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
multiscale kernel convolution model is assigned a new class of "Tree shrinkage
prior" distributions. Tree shrinkage priors exert increasing shrinkage on the
coefficients as resolution grows so as to adapt to the necessary degree of
resolution at any sub-domain. Our proposed model has a number of significant
features over the existing multi-scale spatial models for big data. In contrast
to the existing multiscale approaches, the proposed approach auto-tunes the
degree of resolution necessary to model a subregion in the domain, achieves
scalability by suitable parallelization of local updating of parameters and is
buttressed by theoretical support. Excellent empirical performances are
illustrated using several simulation experiments and a geostatistical analysis
of the sea surface temperature data from the pacific ocean.
