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Title: Positive definite functions on spheres: Some statistical and mathematical issues Authors:  Pier Giovanni Bissiri - University of Bologna (Italy) [presenting]
Emilio Porcu - Khalifa University (United Arab Emirates)
Felipe Tangle - University of Notre Dame (United States)
Ruben Soza - Pontificia Universidad Catolica (Chile)
Fernando Quintana - Pontificia Universidad Catolica de Chile (Chile)
Abstract: Positive definite functions are a key mathematical tool in geostatistics. If the study region is geographically extensive, the space which needs to be considered is the spherical surface equipped with the geodesic distance. After reviewing some general results about positive definite functions on spheres, the focus is on Bayesian nonparametric models for spatial covariance functions for global data. Then, it will review the main known results about strict positive definiteness on spheres in the isotropic case and will show a recent result in the axially symmetric case.