Density Estimation for Compound Cox Processes on Hyperspheres

Cox multiple scattering processes on hyperspheres are a class of doubly stochastic Poisson processes that can be used to describe scattering phenomenon in Physics (optics, micro-waves, acoustics, etc.). In this article, we present an EM (Expectation Maximization) technique to estimate the concentration parameter of a Compound Cox process with values on hyperspheres. The proposed algorithm is based on an approximation formula for multiconvolution of von Mises Fisher densities on spheres of any dimension.