We study multivariate Gaussian random fields defined over ddimensional 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.

Alegría, A., Bissiri, P., 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 ddimensional 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.
Articolo in rivista - Articolo scientifico
Bivariate climate data; Lp approximations; Matrix-valued covariance function; Multivariate random field; Nonparametric Bayes; Sphere;
English
2021
15
1
2360
2392
open
Alegría, A., Bissiri, P., 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].
File in questo prodotto:
File Dimensione Formato  
Alegría-2021-Electr J Stat-VoR.pdf

accesso aperto

Descrizione: Research Article
Tipologia di allegato: Publisher’s Version (Version of Record, VoR)
Licenza: Creative Commons
Dimensione 840.36 kB
Formato Adobe PDF
840.36 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/443678
Citazioni
  • Scopus 3
  • ???jsp.display-item.citation.isi??? 2
Social impact