Multivariate isotropic random fields on spheres: Nonparametric bayesian modeling and lp fast approximations

Alfredo Alegría, Pier Giovanni Bissiri, Galatia Cleanthous, Emilio Porcu, Philip White

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

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.

Original languageBritish English
Pages (from-to)2360-2392
Number of pages33
JournalElectronic Journal of Statistics
Volume15
Issue number1
DOIs
StatePublished - 2021

Keywords

  • Bivariate climate data
  • L approximations
  • Matrix-valued covariance function
  • Multivariate random field
  • Nonparametric Bayes
  • Sphere

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