A0198
Title: Multivariate isotropic random fields on spheres: Nonparametric Bayesian modeling and $L_p$ fast approximations
Authors: Philip White - Brigham Young University (United States) [presenting]
Pier Giovanni Bissiri - - (Italy)
Emilio Porcu - Khalifa University (United Arab Emirates)
Galatia Cleanthous - National University of Ireland Maynooth (Ireland)
Alfredo Alegria - Universidad Tecnica Federico Santa Maria (Chile)
Abstract: Multivariate Gaussian random fields defined over d-dimensional spheres are studied. 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 accuracy are established. Our findings are supported by 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, we consider a bivariate spatial data set of two 2019 NCEP/NCAR Flux Reanalyses.
