Hierarchical low rank approximation of likelihoods for large spatial datasets

TL;DR

This paper introduces a hierarchical low rank approximation method for likelihood estimation in large, irregularly spaced spatial datasets, significantly improving computational and statistical efficiency in climate data modeling.

Contribution

A novel hierarchical low rank approximation scheme for maximum likelihood estimation that enhances efficiency and accuracy for large spatial datasets.

Findings

Method is theoretically sound and improves statistical efficiency.

Numerical and simulation studies demonstrate superior performance.

Applied to 2 million soil moisture measurements, enabling better climate variability analysis.

Abstract

Datasets in the fields of climate and environment are often very large and irregularly spaced. To model such datasets, the widely used Gaussian process models in spatial statis- tics face tremendous challenges due to the prohibitive computational burden. Various ap- proximation methods have been introduced to reduce the computational cost. However, most of them rely on unrealistic assumptions for the underlying process and retaining statistical efficiency remains an issue. We develop a new approximation scheme for maximum likeli- hood estimation. We show how the composite likelihood method can be adapted to provide different types of hierarchical low rank approximations that are both computationally and statistically efficient. The improvement of the proposed method is explored theoretically; the performance is investigated by numerical and simulation studies; and the practicality is illustrated through applying our methods to 2 million measurements of soil moisture in the area of the Mississippi River basin, which facilitates a better understanding of the climate variability.