Neural autoregressive flows enable flexible high-dimensional spatial warpings for nonstationary anisotropic processes, with simulations showing greater representational capacity than standard models and an application to 3D Argo Floats data.
Review: Nonstationary Spatial Modeling, with Emphasis on Process Convolution and Covariate-Driven Approaches
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abstract
In many environmental applications involving spatially-referenced data, 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 traditionally assumed to belong to a parametric class of stationary models. While convenient, the assumption of stationarity is rarely realistic; as a result, there is a rich literature on alternative methodologies which capture and model the nonstationarity present in most environmental processes. This review document provides a rigorous and concise description of the existing literature on nonstationary methods, paying particular attention to process convolution (also called kernel smoothing or moving average) approaches. A summary is also provided of more recent methods which leverage covariate information and yield both interpretational and computational benefits. Note: the article is borrowed from Chapters 1 and 2 of the author's Ph.D. dissertation, joint with Catherine A. Calder.
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A covariate-driven spatial deformation model for nonstationary GPs is created using Lie algebra velocity fields with truncated covariate interactions, supporting efficient estimation and prediction from limited sample pairs.
A convolution process on a directed network provides a covariance model for SST that respects physical barriers and currents, used to identify thermal hot spots via Monte Carlo RCP projections.
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Modeling nonstationary spatial processes with normalizing flows
Neural autoregressive flows enable flexible high-dimensional spatial warpings for nonstationary anisotropic processes, with simulations showing greater representational capacity than standard models and an application to 3D Argo Floats data.
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Predicting Covariate-Driven Spatial Deformation for Nonstationary Gaussian Processes
A covariate-driven spatial deformation model for nonstationary GPs is created using Lie algebra velocity fields with truncated covariate interactions, supporting efficient estimation and prediction from limited sample pairs.
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A Convolution Process for Sea Surface Temperature Hot-Spot Identification in the Mediterranean Sea
A convolution process on a directed network provides a covariance model for SST that respects physical barriers and currents, used to identify thermal hot spots via Monte Carlo RCP projections.