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Abstract:
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With the proliferation of modern high-resolution measuring instruments mounted on satellites, planes, ground-based vehicles and monitoring stations, a need has arisen for statistical methods suitable for the analysis of large spatial datasets observed on large spatial domains, where nonstationarity is to be expected.
We start with a model combining a low-dimensional component, which allows for flexible modeling of long-range dependence via a set of spatial basis functions, with a fine-scale-variation component, which allows for modeling of local dependence using a compactly supported covariance function. We then propose two extensions to this model that result in increased flexibility: First, the model is parameterized based on a nonstationary Matern covariance, where the parameters vary smoothly across space. Second, in our fully Bayesian model, all components and parameters are considered random, including the number, locations, and shapes of the basis functions used in the low-rank component.
Using simulated data and a real-world dataset of high-resolution soil measurements, we show that both extensions can result in substantial improvements over the current state-of-the-art.
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