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

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