Otto’s metric on location-scale models and warped Riemannian metric

Abstract

In this paper, we show that the Otto’s metric on a location- scale model defined on a Riemannian manifold is a warped Riemannian metric. This has been done by assuming that the location-scale model is invariant under the action of some Lie group. The obtained result is applied to the von Mises-Fisher model and to the Riemannian Gaussian model