Parallel Approximation of the Tukey G-and-H Likelihoods for Large-Scale Non-Gaussian Geostatistical Modeling

• Activity Number: 426 - Computing in Large and Complex Data Analysis
• Type: Contributed
• Date/Time: Wednesday, August 10, 2022 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Sagnik Mondal* and Sameh Abdulah and Hatem Ltaief and Ying Sun and Marc Genton and David Keyes
• Companies: King Abdullah University of Science and Technology and KAUST and KAUST and KAUST and KAUST and King Abdullah University of Science and Technology
• Keywords: Tukey g-and-h random field; Parallel computing; Gaussian log-likelihood; High performance computing; Tile low rank approximation of Gaussian log-likelihood; Large-scale spatial statistics application

Abstract

Gaussian random fields are among the most popular models to describe spatial data. However, the assumption of Gaussianity in real data is unrealistic since data may show signs of skewness and heavy tails. Herein, we consider the Tukey g-and-h (TGH) non-Gaussian random field that shows more robustness in modeling spatial data by including two parameters to incorporate skewness and heavy tail features. This modeling process involves generating a dense symmetric positive definite matrix with O(n^2) space complexity and O(n^3) operational complexity, where n represents the number of spatial locations. On a large scale, this modeling process becomes prohibitive with standard methods. This work provides a parallel high-performance implementation of the TGH random field's inference on state-of-the-art hardware architectures. The implementation permits running the exact non-Gaussian modeling process for a large number of geospatial locations. We also provide a Tile Low-Rank approximation implementation that can accelerate the execution compared to the exact solution by around 7.29X and 2.96X on shared memory and distributed memory systems, respectively, using up to 810K spatial locations.