A General Class of Outage Error Probability Lower Bounds in Bayesian Parameter Estimation

Abstract

In this paper, a new class of lower bounds on the outage error probability in Bayesian parameter estimation is proposed. The outage error probability is an important criterion in parameter estimation that provides meaningful information even in the presence of large errors and is useful for prediction of the system operation region. Computation of the minimum outage error probability is usually not tractable and thus, lower bounds on this probability can be very useful for performance analysis. The proposed class of lower bounds on the outage error probability is derived using Holder's inequality. Several bounds in the proposed class are presented. It is shown that the Ziv-Zakai lower bound on the outage error probability can be obtained from a subclass in the proposed class of bounds. The proposed class of bounds is utilized to derive a new class of Bayesian bounds on the mean-square error. It is shown that, for unimodal posterior probability density functions, the tightest lower bound on the probability of outage error in the proposed class attains the minimum probability of outage error. The proposed bounds are exemplified in linear Gaussian model parameter estimation and time-delay estimation.