2020/01/17 by Hou‐Cheng Yang, Yang, Hou-Cheng, Jonathan R. Bradley +1
Computer Science · Economics, Econometrics and Finance · Environmental Science · #FOS: Computer and information sciences #Geochemistry and Geologic Mapping #Methodology (stat.ME) #Soil Geostatistics and Mapping #Spatial and Panel Data Analysis
paper · pdf · doi:10.48550/arxiv.2001.06477
openalex publication_date 2020/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is increasingly understood that the assumption of stationarity is unrealistic for many spatial processes. In this article, we combine dimension expansion with a spectral method to model big non-stationary spatial fields in a computationally efficient manner. Specifically, we use Mejia and Rodriguez-Iturbe (1974)'s spectral simulation approach to simulate a spatial process with a covariogram at locations that have an expanded dimension. We introduce Bayesian hierarchical modelling to dimension expansion, which originally has only been modeled using a method of moments approach. In particular, we simulate from the posterior distribution using a collapsed Gibbs sampler. 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 National Aeronautics and Space Administration (NASA).