Large Multi-scale Spatial Kriging Using Tree Shrinkage Priors

TL;DR

This paper introduces a multiscale spatial kriging method with tree shrinkage priors that adaptively determines resolution levels, enabling scalable and precise modeling of large spatial datasets.

Contribution

It proposes a novel multiscale kernel convolution model with tree shrinkage priors that automatically tune resolution and improve scalability for big spatial data.

Findings

Effective in capturing fine and large scale features.

Achieves scalability through parallel local updates.

Demonstrates superior performance in simulations and real data.

Abstract

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.