Wrapped statistical models on manifolds: motivations, the case SE(n), and generalization to symmetric spaces

We address here the construction of wrapped probability densities on Lie groups and quotient of Lie groups using the exponential map. The paper starts by briefly reviewing the different approaches to build densities on a manifold and shows the interest of wrapped distributions. We then construct wrapped densities on SE(n) and discuss their statistical estimation. We conclude by an opening to the case of symmetric spaces.