Some Inequalities Between Pairs of Marginal and Joint Bayesian Lower Bounds

Bacharach, Lucien
Chaumette, Eric
Fritsche, Carsten
Orguner, Umut
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 illustrate the tightness relations.


On generalized integral inequalities with applications in bio-mathematics and physical sciences
Pelen, Neslihan Nesliye; Önsiper, Mustafa Hurşit; Güvenilir, Ayşe Feza; Department of Mathematics (2015)
In this thesis, applications of generalized integral inequalities especially on biomathematics and physics are studied. Application on Biomathematics is about the predatorprey dynamic systems with Beddington DeAngelis type functional response and application on physics is about water percolation equation. This thesis consists 6 chapters. Chapter 1 is introductory and contains the thesis structure. Chapter 2 is about under which conditions the two dimensional predator-prey dynamic system with Beddington DeAn...
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.
Singular inverse Sturm-Liouville problems with Hermite pseudospectral methods
Altundag, H.; Taşeli, Hasan (2021-10-01)
A numerical approximation to recover certain symmetric potentials in the singular inverse Sturm-Liouville problems over (-infinity,infinity) is presented. A Hermite pseudospectral method is employed to cope with the corresponding direct problem on the real line, which is encountered in the iterative procedure proposed for the inverse problem. The usual but unwelcome ill-posed structure of the resulting numerical algorithm has been treated to some extent by the help of a flexible optimization parameter and r...
Accurate numerical bounds for the spectral points of singular Sturm-Liouville problems over 0 < x < infinity
Taşeli, Hasan (Elsevier BV, 2004-03-01)
The eigenvalues of singular Sturm-Liouville problems defined over the semi-infinite positive real axis are examined on a truncated interval 0<x<l as functions of the boundary point l. As a basic theoretical result, it is shown that the eigenvalues of the truncated interval problems satisfying Dirichlet and Neumann boundary conditions provide, respectively, upper and lower bounds to the eigenvalues of the original problem. Moreover, the unperturbed system in a perturbation problem, where l remains sufficient...
Almost periodic solutions of the linear differential equation with piecewise constant argument
Akhmet, Marat (2009-10-01)
The paper is concerned with the existence and stability of almost periodic solutions of linear systems with piecewise constant argument where t∈R, x ∈ Rn [·] is the greatest integer function. The Wexler inequality [1]-[4] for the Cauchy's matrix is used. The results can be easily extended for the quasilinear case. A new technique of investigation of equations with piecewise argument, based on an integral representation formula, is proposed. Copyright © 2009 Watam Press.
Citation Formats
L. Bacharach, E. Chaumette, C. Fritsche, and U. Orguner, “Some Inequalities Between Pairs of Marginal and Joint Bayesian Lower Bounds,” 2019, Accessed: 00, 2020. [Online]. Available: