Intrinsic Bayesian Cram\'er-Rao Bound with an Application to Covariance Matrix Estimation

arXiv:2311.04748v2 Announce Type: replace-cross
Abstract: This paper presents a new performance bound for estimation problems where the parameter to estimate lies in a Riemannian manifold (a smooth manifold endowed with a Riemannian metric) and follows a given prior distribution. In this setup, the chosen Riemannian metric induces a geometry for the parameter manifold, as well as an intrinsic notion of the estimation error measure. Performance bound for such error measure were previously obtained in the non-Bayesian case (when the unknown …

abstract application arxiv bayesian covariance cs.lg distribution geometry intrinsic lies manifold math.st matrix paper performance prior replace setup stat.ap stat.ml stat.th type