Combining spatial information sources while accounting for systematic errors in proxies

TL;DR

This paper develops a flexible hierarchical model using Markov random field approximations to better account for systematic errors in high-dimensional environmental proxies, specifically satellite aerosol and atmospheric model outputs for air pollution.

Contribution

It introduces a novel, computationally efficient discrepancy modeling approach that captures small-scale errors in proxies, addressing identifiability issues in environmental data integration.

Findings

Discrepancies occur at various spatial scales, especially small-scale.

Modeling the discrepancy does not significantly improve prediction accuracy.

Identifiability issues limit the benefits of using proxies for prediction.

Abstract

Environmental research increasingly uses high-dimensional remote sensing and numerical model output to help fill space-time gaps between traditional observations. Such output is often a noisy proxy for the process of interest. Thus one needs to separate and assess the signal and noise (often called discrepancy) in the proxy given complicated spatio-temporal dependencies. Here I extend a popular two-likelihood hierarchical model using a more flexible representation for the discrepancy. I employ the little-used Markov random field approximation to a thin plate spline, which can capture small-scale discrepancy in a computationally efficient manner while better modeling smooth processes than standard conditional auto-regressive models. The increased flexibility reduces identifiability, but the lack of identifiability is inherent in the scientific context. I model particulate matter air pollution using satellite aerosol and atmospheric model output proxies. The estimated discrepancies occur at a variety of spatial scales, with small-scale discrepancy particularly important. The examples indicate little predictive improvement over modeling the observations alone. Similarly, in simulations with an informative proxy, the presence of discrepancy and resulting identifiability issues prevent improvement in prediction. The results highlight but do not resolve the critical question of how best to use proxy information while minimizing the potential for proxy-induced error.