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2021 Multivariate isotropic random fields on spheres: Nonparametric Bayesian modeling and Lp fast approximations
Alfredo Alegría, Pier Giovanni Bissiri, Galatia Cleanthous, Emilio Porcu, Philip White
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Electron. J. Statist. 15(1): 2360-2392 (2021). DOI: 10.1214/21-EJS1842

Abstract

We study multivariate Gaussian random fields defined over d-dimensional spheres. First, we provide a nonparametric Bayesian framework for modeling and inference on matrix-valued covariance functions. We determine the support (under the topology of uniform convergence) of the proposed random matrices, which cover the whole class of matrix-valued geodesically isotropic covariance functions on spheres. We provide a thorough inspection of the properties of the proposed model in terms of (a) first moments, (b) posterior distributions, and (c) Lipschitz continuities. We then provide an approximation method for multivariate fields on the sphere for which measures of Lp accuracy are established. Our findings are supported through simulation studies that show the rate of convergence when truncating a spectral expansion of a multivariate random field at a finite order. To illustrate the modeling framework developed in this paper, we consider a bivariate spatial data set of two 2019 NCEP/NCAR Flux Reanalyses.

Acknowledgments

Alfredo Alegría and Emilio Porcu are supported by the National Agency for Research and Development, Chile, through grants CONICYT-ANID/FONDECYT/INICIACIÓN/No. 11190686 (A. Alegría) andCONICYT-ANID/FONDECYT/REGULAR/No. 1170290 (E. Porcu).

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Alfredo Alegría. Pier Giovanni Bissiri. Galatia Cleanthous. Emilio Porcu. Philip White. "Multivariate isotropic random fields on spheres: Nonparametric Bayesian modeling and Lp fast approximations." Electron. J. Statist. 15 (1) 2360 - 2392, 2021. https://doi.org/10.1214/21-EJS1842

Information

Received: 1 April 2020; Published: 2021
First available in Project Euclid: 28 April 2021

Digital Object Identifier: 10.1214/21-EJS1842

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Vol.15 • No. 1 • 2021
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