A class of Weiss-Weinstein bounds and its relationship with the Bobrovsky-Mayer-Wolf-Zakai bounds

TL;DR

This paper introduces a broad class of Bayesian lower bounds related to Weiss-Weinstein bounds, connecting them with the Bobrovsky-Mayer-Wolf-Zakai bounds and proposing regularized forms for constrained parameter sets.

Contribution

It generalizes Bayesian large-error bounds, links them to existing bounds like BMZB, and proposes regularized bounds for constrained support scenarios.

Findings

Generalized bounds are essentially free from regularity conditions.

The limiting form of these bounds yields the generalized Bayesian Cramer-Rao bound.

Proposed bounds show potential for increased tightness in the threshold region.

Abstract

A fairly general class of Bayesian "large-error" lower bounds of the Weiss-Weinstein family, essentially free from regularity conditions on the probability density functions support, and for which a limiting form yields a generalized Bayesian Cramer-Rao bound (BCRB), is introduced. In a large number of cases, the generalized BCRB appears to be the Bobrovsky-Mayer-Wolf-Zakai bound (BMZB). Interestingly enough, a regularized form of the Bobrovsky-Zakai bound (BZB), applicable when the support of the prior is a constrained parameter set, is obtained. Modified Weiss-Weinstein bound and BZB which limiting form is the BMZB are proposed, in expectation of an increased tightness in the threshold region. Some of the proposed results are exemplified with a reference problem in signal processing: the Gaussian observation model with parameterized mean and uniform prior.