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

Zvika Ben-Haim; Yonina C. Eldar

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arXiv · 0804.4391

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

Zvika Ben-Haim·Yonina C. Eldar

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Abstract

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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Zvika Ben-Haim, Yonina C. Eldar. 2009-05-27. A Lower Bound on the Bayesian MSE Based on the Optimal Bias Function. https://arxiv.org/abs/0804.4391

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