🤖 AI Summary
To address computational bottlenecks and high-dimensional parameter inference in modeling nonstationary spatial processes, this paper proposes a scalable full Bayesian framework. First, it introduces an analytically tractable representation based on spatially varying covariance kernels to explicitly capture local dependence structures. Second, it designs a nested alternating hybrid Hamiltonian Monte Carlo (HMC) algorithm to enable efficient and stable posterior sampling at large spatial scales. Third, it integrates formal model selection with parameter identifiability analysis to ensure inferential reliability. The framework demonstrates parameter identifiability and posterior consistency on synthetic data. On real-world applications—NDVI remote sensing and soil lead contamination datasets—it achieves significant improvements in predictive accuracy and uncertainty quantification quality. By unifying theoretical rigor with computational scalability, the approach establishes a new paradigm for modeling complex geospatial data.
📝 Abstract
Spatial process models for capturing nonstationary behavior in scientific data present several challenges with regard to statistical inference and uncertainty quantification. While nonstationary spatially-varying kernels are attractive for their flexibility and richness, their practical implementation has been reported to be overwhelmingly cumbersome because of the high-dimensional parameter spaces resulting from the spatially varying process parameters. Matters are considerably exacerbated with the massive numbers of spatial locations over which measurements are available. With limited theoretical tractability offered by nonstationary spatial processes, overcoming such computational bottlenecks require a synergy between model construction and algorithm development. We build a class of scalable nonstationary spatial process models using spatially varying covariance kernels. We present some novel consequences of such representations that befit computationally efficient implementation. More specifically, we operate within a coherent Bayesian modeling framework to achieve full uncertainty quantification using a Hybrid Monte-Carlo with nested interweaving. We carry out experiments on synthetic data sets to explore model selection and parameter identifiability and assess inferential improvements accrued from the nonstationary modeling. We illustrate strengths and pitfalls with a data set on remote sensed normalized difference vegetation index with further analysis of a lead contamination data set in the Supplement.