General classes of Bayesian lower bounds for outage error probability and MSE

In this paper, new classes of lower bounds on the outage error probability and on the minimum mean-square-error (MSE) in Bayesian parameter estimation are proposed. The outage error probability and the MSE are important criteria in parameter estimation. However, computation of these terms is usually not tractable. The proposed outage error probability class of lower bounds is derived using reverse Hölder inequality. This class is utilized to derive a new class of Bayesian MSE bounds. It is shown that the tightest bound from the proposed class is achieved by the generalized maximum a-posteriori probability (MAP) estimation. In addition, for unimodal symmetric conditional probability density functions, the tightest MSE bound in this class coincides with the minimum MSE (MMSE) obtained by the conditional expectation estimator. It is proved that the tightest MSE bound in this class is always tighter than the Ziv-Zakai lower bounds.