# Reduced Basis Kriging for Big Spatial Fields

## TL;DR

This paper introduces a computationally efficient method for spatial prediction in large Gaussian random fields by combining fixed rank kriging with sparse matrix techniques, enabling faster processing without sacrificing accuracy.

## Contribution

It develops a novel approach that enhances fixed rank kriging using restricted maximum likelihood and sparse matrices for better efficiency on big spatial datasets.

## Key findings

- Achieves faster computation with maintained prediction accuracy.
- Successfully applied to large climate datasets with excellent results.
- Provides a scalable solution for spatial prediction in big data contexts.

## Abstract

In spatial statistics, a common method for prediction over a Gaussian random field (GRF) is maximum likelihood estimation combined with kriging. For massive data sets, kriging is computationally intensive, both in terms of CPU time and memory, and so fixed rank kriging has been proposed as a solution. The method however still involves operations on large matrices, so we develop an alteration to this method by utilizing the approximations made in fixed rank kriging combined with restricted maximum likelihood estimation and sparse matrix methodology. Experiments show that our methodology can provide additional gains in computational efficiency over fixed-rank kriging without loss of accuracy in prediction. The methodology is applied to climate data archived by the United States National Climate Data Center, with very good results.