Abstract
We consider Gaussian random fields on the product of spheres. We study the regularity and the Hölder continuity of such random fields via their covariance function. Moreover, we approximate the Gaussian random fields using truncations of the Karhunen-Loéve expansion and conduct simulation experiments to illustrate our approximation results. Using hourly wind speed and global space-time cloud cover datasets, we discuss modelling data in a Bayesian framework using Gaussian random fields over the product of spheres with covariance approximations through truncated series expansions.
Funding Statement
Alfredo Alegría acknowledges the funding of the National Agency for Research and Development of Chile, through grant ANID/FONDECYT/INICIACIÓN/No. 11190686.
Galatia Cleanthous has been supported by the individual grant “New function spaces in harmonic analysis and their applications in Statistics”, from the University of Cyprus.
Citation
Alfredo Alegría. Galatia Cleanthous. Athanasios G. Georgiadis. Emilio Porcu. Philip A. White. "Gaussian random fields on the product of spheres: Theory and applications." Electron. J. Statist. 18 (1) 1394 - 1435, 2024. https://doi.org/10.1214/24-EJS2231
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