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A lower bound on the minimum mean-squared error (MSE) in a Bayesianestimation problem is proposed in this paper. This bound utilizes a well-knownconnection to the deterministic estimation setting. Using the priordistribution, the bias function which minimizes the Cramer-Rao bound can bedetermined, resulting in a lower bound on the Bayesian MSE. The bound isdeveloped for the general case of a vector parameter with an arbitraryprobability distribution, and is shown to be asymptotically tight in both thehigh and low signal-to-noise ratio regimes. A numerical study demonstratesseveral cases in which the proposed technique is both simpler to compute andtighter than alternative methods.

A Lower Bound on the Bayesian MSE Based on the Optimal Bias Function