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.
@article{arxiv.0804.4391,
title = {A Lower Bound on the Bayesian MSE Based on the Optimal Bias Function},
author = {Zvika Ben-Haim and Yonina C. Eldar},
journal= {arXiv preprint arXiv:0804.4391},
year = {2009}
}
Comments
18 pages, 3 figures. Accepted for publication in IEEE Transactions on Information Theory