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 L^p 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 FluxReanalyses.

Alegría, A., Bissiri, P.G., Cleanthous, G., Porcu, E., White, P. (2021). Multivariate isotropic random fields on spheres: Nonparametric Bayesian modeling and Lp fast approximations. ELECTRONIC JOURNAL OF STATISTICS, 15(1), 2360-2392 [10.1214/21-EJS1842].

Multivariate isotropic random fields on spheres: Nonparametric Bayesian modeling and Lp fast approximations

Bissiri, Pier Giovanni;
2021

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 L^p 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 FluxReanalyses.
2021
Alegría, A., Bissiri, P.G., Cleanthous, G., Porcu, E., White, P. (2021). Multivariate isotropic random fields on spheres: Nonparametric Bayesian modeling and Lp fast approximations. ELECTRONIC JOURNAL OF STATISTICS, 15(1), 2360-2392 [10.1214/21-EJS1842].
Alegría, Alfredo; Bissiri, Pier Giovanni; Cleanthous, Galatia; Porcu, Emilio; White, Philip
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/819522
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