This paper considers Cramer-Rao type bounds for the estimation error of a parameter in a Bayesian setup. This class of bounds, introduced by Van Trees, proved useful in various stochastic communications and control problems. Two issues are considered in this paper. The first deals with a comparison of the tightness of several different versions of the bound in the multivariate case. The second introduces several useful generalizations of the original version of the bound.
"Some Classes of Global Cramer-Rao Bounds." Ann. Statist. 15 (4) 1421 - 1438, December, 1987. https://doi.org/10.1214/aos/1176350602