The 19th Statistical Machine Learning Seminar (2014.9.11)

The 19th Statistical Machine Learning Seminar
Date/time: Sep 11 (Thu) 15:00-
Place: Seminar Room 5 (3F, D313),
Institute of Statistical Mathematics (Tachikawa, Tokyo)
Title: von Mises-Fisher and Compound Cox processes on hyperspheres
Speaker: Nicolas Le Bihan, CNRS and University of Melbourne
abstract: In this talk, we present several results about isotropic
random walks and Compound Cox Processes (CCP) on hyperspheres S^{p-1}
in R^p . Unimodality for the multiconvolution of symmetrical
probability density functions (pdf) on S^{p-1} will be introduced and
used together with Fourier expansion results to provide explicit
expression of the pdf of multiple scattering processes on hyperspheres.
Such processes will then be studied in the case where the scattering
distribution is von Mises-Fisher (vMF). Asymptotic distributions for
the multiconvolution of vMFs on S^{p-1} will be used to provide
expression of the distribution of the multiple scattering process.
Finally, both Fourier expansion and asymptotic approximation allow to
compute estimation bounds for the parameters of Compound Cox Processes
(CCP) on S^{p-1}.
This is a joint work with Florent Chatelain (Gipsa-Lab, Grenoble) and
J.H. Manton (University of Melbourne).