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Nonparametric Bayesian modelling of longitudinally integrated covariance functions on spheres

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

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.

Suggested Citation

  • Bissiri, Pier Giovanni & Cleanthous, Galatia & Emery, Xavier & Nipoti, Bernardo & Porcu, Emilio, 2022. "Nonparametric Bayesian modelling of longitudinally integrated covariance functions on spheres," Computational Statistics & Data Analysis, Elsevier, vol. 176(C).
  • Handle: RePEc:eee:csdana:v:176:y:2022:i:c:s0167947322001359
    DOI: 10.1016/j.csda.2022.107555
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    References listed on IDEAS

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    1. Alexandra M. Schmidt & Anthony O'Hagan, 2003. "Bayesian inference for non‐stationary spatial covariance structure via spatial deformations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(3), pages 743-758, August.
    2. Emilio Porcu & Alfredo Alegria & Reinhard Furrer, 2018. "Modeling Temporally Evolving and Spatially Globally Dependent Data," International Statistical Review, International Statistical Institute, vol. 86(2), pages 344-377, August.
    3. Yanbing Zheng & Jun Zhu & Anindya Roy, 2010. "Nonparametric Bayesian inference for the spectral density function of a random field," Biometrika, Biometrika Trust, vol. 97(1), pages 238-245.
    4. Nicolas Chopin & J. Rousseau & Brunero Liseo, 2013. "Computational aspects of Bayesian spectral density estimation," Post-Print hal-01026131, HAL.
    5. Gelfand, Alan E. & Kottas, Athanasios & MacEachern, Steven N., 2005. "Bayesian Nonparametric Spatial Modeling With Dirichlet Process Mixing," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1021-1035, September.
    6. Peter Müeller & Fernando A. Quintana & Garritt Page, 2018. "Nonparametric Bayesian inference in applications," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(2), pages 175-206, June.
    7. E. Porcu & S. Castruccio & A. Alegría & P. Crippa, 2019. "Axially symmetric models for global data: A journey between geostatistics and stochastic generators," Environmetrics, John Wiley & Sons, Ltd., vol. 30(1), February.
    8. repec:dau:papers:123456789/10785 is not listed on IDEAS
    9. Jason A. Duan & Michele Guindani & Alan E. Gelfand, 2007. "Generalized Spatial Dirichlet Process Models," Biometrika, Biometrika Trust, vol. 94(4), pages 809-825.
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