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

TL;DR

This paper introduces a new lower bound on Bayesian MSE using an optimal bias function, applicable to vector parameters with arbitrary distributions, and demonstrates its tightness and computational advantages over existing methods.

Contribution

It proposes a novel lower bound on Bayesian MSE based on the optimal bias function, applicable to general vector parameters with arbitrary distributions.

Findings

The bound is asymptotically tight in high and low SNR regimes.

The proposed bound is simpler to compute than existing methods.

Numerical results show the bound is tighter in several cases.

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.