Reliable Predictive Resolution in GeospatialModelling

High-resolution geospatial prediction and satellite image downscaling are increasingly enabled by advances in machine learning and the availability of fine-scale covariates. However, predicted maps are often delivered on arbitrary grids that are not justified by the sampling density of observations. While uncertainty can be quantified at unobserved locations, the spatial scales over which predictions are supported by the data and the modelling process are typically not characterized. Besides computational and storage costs, critical consequences including over-interpretation, modelling noise, and most importantly, the apparent predictive resolution of spatial products can be misleading for downstream applications, potentially affecting scientific conclusions. An example is the use of predicted air pollution maps in health cohort studies to assess exposure–response relationships. This raises a fundamental but under-addressed question: what is the finest spatial resolution at which predictions are meaningfully supported by the data (and model)?

We investigate how to meaningfully determine the predictive resolution in regression models by linking sampling density and model parameters in the frequency domain through spectral analysis. Two challenges are 1) to identify the sampling density in the multi-dimensional feature space, where the sampling typically becomes irregular; and 2) how to relate the frequency in the feature space to the spatial resolution. Using simulated and real-world geospatial datasets, we show that some arbitrarily selected output resolutions in existing literatures could exceed the data-supported predictive resolution, and could induce unnoticed biases or change-of-support issues in downstream analyses.