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Abstract:
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In many environmental applications, limitations on the number and locations of observations motivate the need for practical and efficient models for spatial interpolation, or kriging. A key component of models for continuously-indexed spatial data is the covariance function, which is often assumed to belong to a parametric class of stationary models. Alternative methods that more appropriately model the nonstationarity present in environmental processes often involve high-dimensional parameter spaces, which lead to difficulties in model fitting and interpretability. To overcome this issue, we build on the growing literature of covariate-driven nonstationary spatial modeling. Using process convolution techniques, we propose a Bayesian model for continuously-indexed spatial data based on a flexible parametric covariance regression structure for a convolution-kernel covariance matrix. The resulting nonstationary model yields a parsimonious representation and provides a practical compromise between stationary and highly parameterized nonstationary approaches that do not perform well in practice. We illustrate our approach through an analysis of annual precipitation data.
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