  A lower bound on the minimum mean-squared error (MSE) in a Bayesian
estimation problem is proposed in this paper. This bound utilizes a well-known
connection to the deterministic estimation setting. Using the prior
distribution, the bias function which minimizes the Cramer-Rao bound can be
determined, resulting in a lower bound on the Bayesian MSE. The bound is
developed for the general case of a vector parameter with an arbitrary
probability distribution, and is shown to be asymptotically tight in both the
high and low signal-to-noise ratio regimes. A numerical study demonstrates
several cases in which the proposed technique is both simpler to compute and
tighter than alternative methods.
