UCSC-SOE-17-11: Large Multi-Scale Spatial Modeling Using Tree Shrinkage Priors

Rajarshi Guhaniyogi and Bruno Sanso
06/22/2017 10:30 AM
Applied Mathematics & Statistics
We develop a multiscale spatial kernel convolution technique with higher order
functions to capture fi ne 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 signi ficant 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 Paci fic ocean.