Computational Developments and Applications of the Multi-Resolution Approximation for Massive Spatial Data
Date:
Invited Talk. Virtual presentation in section EO58 - “Recent Developments in Spatial Statistics” of Computational and Methodological Statistics (CMStatistics 2021), hosted by King’s College London, UK.
Abstract
Recent developments of computational implementations and applications of the Multi-Resolution Approximation (MRA) spatial model are presented. Prediction and parameter inference are performed via a basis function representation of a Gaussian Process. Firstly, we introduce a parallel version of the MRA in Matlab for distributed computing environments. This implementation builds upon and improves a previous approach, facilitating computations with data sets on the order of 50 million observations while reducing execution times by up to 75%. Secondly, we provide a first glance at extending the MRA to model nonstationarity at a global scale. A basis function representation of covariance function parameters allows us to capture nuanced spatial dependence across large domains. The extension is natural for two reasons: (i) the MRA has been shown to be one of the most computationally efficient and accurate models to analyze large spatial data sets, (ii) the hierarchical domain partitioning imposed by the MRA explicitly defines regions of spatial dependence allowing for careful construction of nonstationary covariance functions. We apply this methodology to global measurements of sea surface temperature data from the Moderate Resolution Imaging Spectroradiometer onboard NASA’s Aqua satellite.