We provide a nonparametric spectral approach to the modeling ofcorrelation functions on spheres. The sequence of Schoenberg coefficients and theirassociated covariance functions are treated as random rather than assuming aparametric form. We propose a stick-breaking representation for the spectrum, andshow that such a choice spans the support of the class of geodesically isotropiccovariance functions under uniform convergence. Further, we examine the firstorder properties of such representation, from which geometric properties can beinferred, in terms of H ̈older continuity, of the associated Gaussian random field.The properties of the posterior, in terms of existence, uniqueness, and Lipschitzcontinuity, are then inspected. Our findings are validated with MCMC simulationsand illustrated using a global data set on surface temperatures.

Nonparametric Bayesian Modeling and Estimation of Spatial Correlation Functions for Global Data

Bissiri, Pier Giovanni;
2021

Abstract

We provide a nonparametric spectral approach to the modeling ofcorrelation functions on spheres. The sequence of Schoenberg coefficients and theirassociated covariance functions are treated as random rather than assuming aparametric form. We propose a stick-breaking representation for the spectrum, andshow that such a choice spans the support of the class of geodesically isotropiccovariance functions under uniform convergence. Further, we examine the firstorder properties of such representation, from which geometric properties can beinferred, in terms of H ̈older continuity, of the associated Gaussian random field.The properties of the posterior, in terms of existence, uniqueness, and Lipschitzcontinuity, are then inspected. Our findings are validated with MCMC simulationsand illustrated using a global data set on surface temperatures.
Porcu, Emilio; Bissiri, Pier Giovanni; Tagle, Felipe; Soza, Rubén; Quintana, Fernando A.
File in questo prodotto:
Eventuali allegati, non sono esposti

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11585/797782
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 0
social impact