Nonparametric Bayesian modelling of longitudinally integrated covariance functions on spheres

Pier Giovanni Bissiri, Galatia Cleanthous, Xavier Emery, Bernardo Nipoti and Emilio Porcu

Computational Statistics & Data Analysis, 2022, vol. 176, issue C

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.

Keywords: Axial symmetry; Bayesian nonparametrics; Covariance functions; Global processes; Longitudinal integration; Data on spheres (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:176:y:2022:i:c:s0167947322001359

DOI: 10.1016/j.csda.2022.107555

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