The turning arcs: a computationally efficient algorithm to simulate isotropic vector-valued Gaussian random fields on the d-sphere
Author
dc.contributor.author
Alegría, Alfredo
Author
dc.contributor.author
Emery, Xavier
Author
dc.contributor.author
Lantuéjoul, Christian
Admission date
dc.date.accessioned
2020-07-02T03:28:17Z
Available date
dc.date.available
2020-07-02T03:28:17Z
Publication date
dc.date.issued
2020
Cita de ítem
dc.identifier.citation
Statistics and Computing Jun 2020
es_ES
Identifier
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10.1007/s11222-020-09952-8
Identifier
dc.identifier.uri
https://repositorio.uchile.cl/handle/2250/175750
Abstract
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Random fields on the sphere play a fundamental role in the natural sciences. This paper presents a simulation algorithm parenthetical to the spectral turning bands method used in Euclidean spaces, for simulating scalar- or vector-valued Gaussian random fields on the d-dimensional unit sphere. The simulated random field is obtained by a sum of Gegenbauer waves, each of which is variable along a randomly oriented arc and constant along the parallels orthogonal to the arc. Convergence criteria based on the Berry-Esseen inequality are proposed to choose suitable parameters for the implementation of the algorithm, which is illustrated through numerical experiments. A by-product of this work is a closed-form expression of the Schoenberg coefficients associated with the Chentsov and exponential covariance models on spheres of dimensions greater than or equal to 2.
es_ES
Patrocinador
dc.description.sponsorship
National Agency for Research and Development of Chile through grant CONICYT/FONDECYT/INICIACION
11190686
National Agency for Research and Development of Chile through grant CONICYT
PIA AFB180004
National Agency for Research and Development of Chile through grant CONICYT/FONDECYT/REGULAR
1170290