  In this paper, new classes of lower bounds on the outage error probability
and on the mean-square-error (MSE) in Bayesian parameter estimation are
proposed. The minima of the h-outage error probability and the MSE are obtained
by the generalized maximum a-posteriori probability and the minimum MSE (MMSE)
estimators, respectively. However, computation of these estimators and their
corresponding performance is usually not tractable and thus, lower bounds on
these terms can be very useful for performance analysis. The proposed class of
lower bounds on the outage error probability is derived using Holder's
inequality. This class is utilized to derive a new class of Bayesian MSE
bounds. It is shown that for unimodal symmetric conditional probability density
functions (pdf) the tightest probability of outage error lower bound in the
proposed class attains the minimum probability of outage error and the tightest
MSE bound coincides with the MMSE performance. In addition, it is shown that
the proposed MSE bounds are always tighter than the Ziv-Zakai lower bound
(ZZLB). The proposed bounds are compared with other existing performance lower
bounds via some examples.
