Open Access
2024 Gaussian random fields on the product of spheres: Theory and applications
Alfredo Alegría, Galatia Cleanthous, Athanasios G. Georgiadis, Emilio Porcu, Philip A. White
Author Affiliations +
Electron. J. Statist. 18(1): 1394-1435 (2024). DOI: 10.1214/24-EJS2231


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.


Download 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.


Received: 1 October 2023; Published: 2024
First available in Project Euclid: 15 March 2024

Digital Object Identifier: 10.1214/24-EJS2231

Primary: 60G60
Secondary: 53A35 , 60G15 , 60G20 , 62F15 , 62P12

Keywords: approximation , covariance kernel , directional data , Hölder continuity , Karhunen-Loéve , seasonal time series , simulations , Sobolev regularity

Vol.18 • No. 1 • 2024
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