General versions of the information inequalities of van Trees and of Stam

Van Trees's inequality is a Bayesian version of the Cramer-Rao inequality for quadratic loss of estimators with values in vector spaces. The first part of the talk presents a generalisation of this inequality to the setting of smooth loss functions and estimators with values in manifolds. Various geometric objects (connections, metrics, tensors) play a role.

Stam's inequality compares the (inverse) Fisher information of the sum of two independent (real-valued) random variables with the (inverse) Fisher informations of these variables. The second part of the talk describes a generalisation of this inequality to the setting of random variables on Lie groups.