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Title: Nonparametric Bayesian modelling of longitudinally integrated covariance functions on the sphere Authors:  Pier Giovanni Bissiri - University of Bologna (Italy)
Galatia Cleanthous - National University of Ireland Maynooth (Ireland)
Xavier Emery - University of Chile (Chile)
Bernardo Nipoti - University of Milan Bicocca (Italy) [presenting]
Emilio Porcu - Khalifa University (United Arab Emirates)
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 which 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 processes on the sphere. We provide 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. We then define and implement a Bayesian nonparametric model for the analysis of data defined on the sphere. We investigate its properties and assess its performance through the analysis of both simulated data and a data set on mean daily air temperatures extracted from the NCEP/NCAR Reanalysis 1 data set.