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Abstract:
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It is increasingly understood that the assumption of stationarity is unrealistic for many spatial processes. For example, in oceanography, environmental, and atmospheric sciences, non-stationarity may occur because of interactions with covariates (e.g., rainfall at one location may occur more around bodies of water even though nearby observations are over land). In this article, we combine dimension expansion with a spectral method to model big non-stationary spatial fields. Specifically, we use Mej ??a and Rodr ??guez-Iturbe (1974)'s spectral approach to approximately simulate from a covariogram at locations that have an expanded dimension. We bring the Bayesian hierarchical framework to dimension expansion, which originally has only been modeled using a method of moments approach. Our method is both full rank and non-stationary, and can be applied to big spatial data because it does not involve storing and inverting large covariance matrices. Additionally, we have fewer parameters than many other non-stationary spatial models. We demonstrate the wide applicability of our approach using a simulation study, and an application using ozone data obtained from the NASA.
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