第19回統計的機械学習セミナー / The 19th Statistical Machine Learning Seminar

Date&Time

2014年9月11日（木）15：00－
/ 11 Sep, 2014 (Thu) 15：00－

Place

統計数理研究所　セミナー室5（3階D313）
/ Seminar Room 5（D313）@ The Institute of Statistical Mathematics

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).