A TIGHTER BAYESIAN CRAMER-RAO BOUND

Date

2019-01-01

Author

Bacharach, Lucien
Fritsche, Carsten
Orguner, Umut
Chaumette, Eric

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

130
views

0
downloads

It has been shown lately that any "standard" Bayesian lower bound (BLB) on the mean squared error (MSE) of the Weiss-Weinstein family (WWF) admits a "tighter" form which upper bounds the "standard" form. Applied to the Bayesian Cramer-Rao bound (BCRB), this result suggests to redefine the concept of efficient estimator relatively to the tighter form of the BCRB, an update supported by a noteworthy example. This paper lays the foundation to revisit some Bayesian estimation problems where the BCRB is not tight in the asymptotic region.

Subject Keywords

Mean Squared Error, Minimum mean squared error, Bayesian cramer-rao bound, Bayesian lower bounds

URI

https://hdl.handle.net/11511/37423

DOI

https://doi.org/10.1109/icassp.2019.8683614

Conference Name

44th IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

Collections

Department of Electrical and Electronics Engineering, Conference / Seminar

Suggestions

OpenMETU
Core

MARGINAL BAYESIAN BHATTACHARYYA BOUNDS FOR DISCRETE-TIME FILTERING Fritsche, Carsten; Orguner, Umut; Özkan, Emre; Gustafsson, Fredrik (2018-04-20) In this paper, marginal versions of the Bayesian Bhattacharyya lower bound (BBLB), which is a tighter alternative to the classical Bayesian Cramer-Rao bound, for discrete-time filtering are proposed. Expressions for the second and third-order marginal BBLBs are obtained and it is shown how these can be approximately calculated using particle filtering. A simulation example shows that the proposed bounds predict the achievable performance of the filtering algorithms better.
Some Inequalities Between Pairs of Marginal and Joint Bayesian Lower Bounds Bacharach, Lucien; Chaumette, Eric; Fritsche, Carsten; Orguner, Umut (2019-01-01) In this paper, tightness relations (or inequalities) between Bayesian lower bounds (BLBs) on the mean-squared-error are derived which result from the marginalization of a joint probability density function (pdf) depending on both parameters of interest and extraneous or nuisance parameters. In particular, it is shown that for a large class of BLBs, the BLB derived from the marginal pdf is at least as tight as the corresponding BLB derived from the joint pdf. A Bayesian linear regression example is used to i...
RESULTS ON THE SUPREMUM OF FRACTIONAL BROWNIAN MOTION Vardar Acar, Ceren (2011-04-01) We show that the distribution of the square of the supremum of reflected fractional Brownian motion up to time a, with Hurst parameter-H greater than 1/2, is related to the distribution of its hitting time to level 1, using the self similarity property of fractional Brownian motion. It is also proven that the second moment of supremum of reflected fractional Brownian motion up to time a is bounded above by a(2H). Similar relations are obtained for the supremum of fractional Brownian motion with Hurst parame...
Maximal matching polytope in trees Tural, Mustafa Kemal (2016-06-01) Given a weighted simple graph, the minimum weighted maximal matching (MWMM) problem is the problem of finding a maximal matching of minimum weight. The MWMM problem is NP-hard in general, but is polynomial-time solvable in some special classes of graphs. For instance, it has been shown that the MWMM problem can be solved in linear time in trees when all the edge weights are equal to one. In this paper, we show that the convex hull of the incidence vectors of maximal matchings (the maximal matching polytope)...
A SUPER-SET OF PATTERSON-WIEDEMANN FUNCTIONS: UPPER BOUNDS AND POSSIBLE NONLINEARITIES Kavut, Selcuk; MAİTRA, Subhamoy; Özbudak, Ferruh (2018-01-01) Construction of Boolean functions on an odd number of variables with nonlinearity exceeding the bent concatenation bound is one of the most difficult combinatorial problems within the domain of Boolean functions. This problem also has deep implications in coding theory and cryptology. Patterson and Wiedemann demonstrated instances of such functions back in 1983. For more than three decades efforts have been channeled into obtaining such instances. For the first time, in this paper we explore nontrivial uppe...

Citation Formats

L. Bacharach, C. Fritsche, U. Orguner, and E. Chaumette, “A TIGHTER BAYESIAN CRAMER-RAO BOUND,” presented at the 44th IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Brighton, England, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/37423.