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.


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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.
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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...
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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...
Decomposition of the mean squared error and NSE performance criteria: Implications for improving hydrological modelling
Gupta, Hoshin V.; Kling, Harald; Yılmaz, Koray Kamil; Martinez, Guillermo F. (2009-10-20)
The mean squared error (MSE) and the related normalization, the Nash-Sutcliffe efficiency (NSE), are the two criteria most widely used for calibration and evaluation of hydrological models with observed data. Here, we present a diagnostically interesting decomposition of NSE (and hence MSE), which facilitates analysis of the relative importance of its different components in the context of hydrological modelling, and show how model calibration problems can arise due to interactions among these components. T...
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: