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.Comment: 5 figures, 2 table
