Nonstationary Nearest Neighbor Gaussian Process: hierarchical model architecture and MCMC sampling
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Nonstationary spatial modeling presents several challenges including, but not limited to, computational cost, the complexity and lack of interpretation of multi-layered hierarchical models, and the challenges in model assessment and selection. This manuscript develops a class of nonstationary Nearest Neighbor Gaussian Process (NNGP) models. NNGPs are a good starting point to address the problem of the computational cost because of their accuracy and affordability. We study the behavior of NNGPs that use a nonstationary covariance function, exploring their properties and the impact of ordering on the effective covariance induced by NNGPs. To simplify spatial data analysis and model selection, we introduce an interpretable hierarchical model architecture, where, in particular, we make parameter interpretation and model selection easier by integrating stationary range, nonstationary range with circular parameters, and nonstationary range with elliptic parameters within a coherent probabilistic structure. Given the NNGP approximation and the model framework, we propose a MCMC implementation based on Hybrid Monte-Carlo and nested interweaving of parametrizations. We carry out experiments on synthetic data sets to explore model selection and parameter identifiability and assess inferential improvements accrued from the nonstationary model. Finally, we use those guidelines to analyze a data set of lead contamination in the United States of America.
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