Taking into account axial symmetry in the covariance function of a Gaussian random field is essential when the purpose is modelling data defined over a large portion of the sphere representing our planet. Axially symmetric covariance functions admit a convoluted spectral representation that makes modelling and inference difficult. This motivates the interest in devising alternative strategies to attain axial symmetry, an appealing option being longitudinal integration of isotropic random fields on the sphere. This paper provides a comprehensive theoretical framework to model longitudinal integration on spheres through a nonparametric Bayesian approach. Longitudinally integrated covariances are treated as random objects, where the randomness is implied by the randomised spectrum associated with the covariance function. After investigating the topological support induced by our construction, we give the posterior distribution a thorough inspection. A Bayesian nonparametric model for the analysis of data defined on the sphere is described and implemented, its performance investigated by means of the analysis of both simulated and real data sets.

Bissiri, P., Cleanthous, G., Emery, X., Nipoti, B., Porcu, E. (2022). Nonparametric Bayesian modelling of longitudinally integrated covariance functions on spheres. COMPUTATIONAL STATISTICS & DATA ANALYSIS, 176(December 2022) [10.1016/j.csda.2022.107555].

Nonparametric Bayesian modelling of longitudinally integrated covariance functions on spheres

Nipoti B.;
2022

Abstract

Taking into account axial symmetry in the covariance function of a Gaussian random field is essential when the purpose is modelling data defined over a large portion of the sphere representing our planet. Axially symmetric covariance functions admit a convoluted spectral representation that makes modelling and inference difficult. This motivates the interest in devising alternative strategies to attain axial symmetry, an appealing option being longitudinal integration of isotropic random fields on the sphere. This paper provides a comprehensive theoretical framework to model longitudinal integration on spheres through a nonparametric Bayesian approach. Longitudinally integrated covariances are treated as random objects, where the randomness is implied by the randomised spectrum associated with the covariance function. After investigating the topological support induced by our construction, we give the posterior distribution a thorough inspection. A Bayesian nonparametric model for the analysis of data defined on the sphere is described and implemented, its performance investigated by means of the analysis of both simulated and real data sets.
Articolo in rivista - Articolo scientifico
Axial symmetry; Bayesian nonparametrics; Covariance functions; Data on spheres; Global processes; Longitudinal integration;
English
Bissiri, P., Cleanthous, G., Emery, X., Nipoti, B., Porcu, E. (2022). Nonparametric Bayesian modelling of longitudinally integrated covariance functions on spheres. COMPUTATIONAL STATISTICS & DATA ANALYSIS, 176(December 2022) [10.1016/j.csda.2022.107555].
File in questo prodotto:
File Dimensione Formato  
Bissiri-2022-Comput Stat Data Anal-VoR.pdf

Solo gestori archivio

Descrizione: Research Article
Tipologia di allegato: Publisher’s Version (Version of Record, VoR)
Dimensione 2.01 MB
Formato Adobe PDF
2.01 MB Adobe PDF   Visualizza/Apri   Richiedi una copia

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/10281/396631
Citazioni
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
Social impact