  A general class of Bayesian lower bounds when the underlying loss function is
a Bregman divergence is demonstrated. This class can be considered as an
extension of the Weinstein--Weiss family of bounds for the mean squared error
and relies on finding a variational characterization of Bayesian risk. The
approach allows for the derivation of a version of the Cram\'er--Rao bound that
is specific to a given Bregman divergence. The new generalization of the
Cram\'er--Rao bound reduces to the classical one when the loss function is
taken to be the Euclidean norm. The effectiveness of the new bound is evaluated
in the Poisson noise setting and the Binomial noise setting.
