Bernoulli Lecture - Strictly and non-strictly positive definite functions on spheres - revisited

In classical papers, Iso Schoenberg (1938, 1942) laid the ground for the study of isotropic positive definite functions on Euclidean spaces and spheres, respectively. Subsequently, positive definite functions on Euclidean spaces have been studied extensively in spatial statistics and related fields. In contrast, positive definite functions on spheres have only recently moved into focus, motivated by critical applied problems in the environmental and geophysical sciences that require correlation models on the surface of Planet Earth. I will review recent progress in the area, with an eye on a listing of 18 open problems posed in 2013.

Part of the Semester : Functional Data Analysis