TY - GEN

T1 - General classes of Bayesian lower bounds for outage error probability and MSE

AU - Routtenberg, Tirza

AU - Tabrikian, Joseph

PY - 2009/12/25

Y1 - 2009/12/25

N2 - 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.

AB - 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.

KW - Bayesian parameter estimation

KW - Maximum a-posteriori probability (MAP)

KW - Mean-square-error (MSE)

KW - Performance lower bounds

KW - Probability of outage error

UR - http://www.scopus.com/inward/record.url?scp=72349095540&partnerID=8YFLogxK

U2 - 10.1109/SSP.2009.5278638

DO - 10.1109/SSP.2009.5278638

M3 - Conference contribution

AN - SCOPUS:72349095540

SN - 9781424427109

T3 - IEEE Workshop on Statistical Signal Processing Proceedings

SP - 69

EP - 72

BT - 2009 IEEE/SP 15th Workshop on Statistical Signal Processing, SSP '09

T2 - 2009 IEEE/SP 15th Workshop on Statistical Signal Processing, SSP '09

Y2 - 31 August 2009 through 3 September 2009

ER -