Incorporating Subsampling into Bayesian Models for High-Dimensional Spatial Data

TL;DR

This paper introduces the spatial data subset model (SDSM), a subsampling method for high-dimensional spatial data that reduces computation time without additional restrictive assumptions, applicable to large datasets.

Contribution

The paper develops and analyzes the SDSM approach, enabling efficient Bayesian spatial modeling on big data without sacrificing statistical properties.

Findings

SDSM provides computational efficiency for large spatial datasets.

The method maintains key spatial statistical properties.

Successful application to real satellite temperature data.

Abstract

Additive spatial statistical models with weakly stationary process assumptions have become standard in spatial statistics. However, one disadvantage of such models is the computation time, which rapidly increases with the number of data points. The goal of this article is to apply an existing subsampling strategy to standard spatial additive models and to derive the spatial statistical properties. We call this strategy the ''spatial data subset model'' (SDSM) approach, which can be applied to big datasets in a computationally feasible way. Our approach has the advantage that one does not require any additional restrictive model assumptions. That is, computational gains increase as model assumptions are removed when using our model framework. This provides one solution to the computational bottlenecks that occur when applying methods such as Kriging to ''big data''. We provide several properties of this new spatial data subset model approach in terms of moments, sill, nugget, and range under several sampling designs. An advantage of our approach is that it subsamples without throwing away data, and can be implemented using datasets of any size that can be stored. We present the results of the spatial data subset model approach on simulated datasets, and on a large dataset consists of 150,000 observations of daytime land surface temperatures measured by the MODIS instrument onboard the Terra satellite.