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

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

2008-04-28

arxiv.org/abs/0804.4391v2

Computer Science

Information Theory

18 pages, 3 figures. Accepted for publication in IEEE Transactions on Information Theory

Scientific paper

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.

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