Non-Stationary Covariance Estimation using the Stochastic Score Approximation for Large Spatial Data

TL;DR

This paper presents a scalable computational approach for estimating complex non-stationary spatial models in large datasets, using stochastic score approximation and a flexible boundary selection procedure.

Contribution

It introduces a novel stochastic score approximation method for non-stationary spatial models that reduces computational complexity to O(n log n) operations.

Findings

Effective estimation of non-stationary models demonstrated through simulations.

Method achieves computational efficiency suitable for large spatial datasets.

Application to arsenic accumulation illustrates practical utility.

Abstract

We introduce computational methods that allow for effective estimation of a flexible, parametric non-stationary spatial model when the field size is too large to compute the multivariate normal likelihood directly. In this method, the field is defined as a weighted spatially varying linear combination of a globally stationary process and locally stationary processes. Often in such a model, the difficulty in its practical use is in the definition of the boundaries for the local processes, and therefore we describe one such selection procedure that generally captures complex non-stationary relationships. We generalize the use of stochastic approximation to the score equations for data on a partial grid in this non-stationary case and provide tools for evaluating the approximate score in $O(n\log n)$ operations and $O(n)$ storage. We perform various simulations to explore the effectiveness and speed of the proposed methods and conclude by making inference on the accumulation behavior of arsenic applied to a sand grain.