On the posterior pointwise convergence rate of a Gaussian signal under a conjugate prior

2009 ◽  
Vol 79 (5) ◽  
pp. 670-675 ◽  
Author(s):  
Alexandra Babenko ◽  
Eduard Belitser
Keyword(s):  
Convergence Rate ◽  
Pointwise Convergence ◽  
Conjugate Prior ◽  
Gaussian Signal

scholarly journals Jump or kink: on super-efficiency in segmented linear regression breakpoint estimation

Biometrika ◽  
2020 ◽  
Author(s):  
Yining Chen
Keyword(s):  
Structural Change ◽  
Linear Regression ◽  
Convergence Rate ◽  
Pointwise Convergence ◽  
Mean Absolute Error ◽  
Absolute Error ◽  
The Other ◽  
Fixed Parameter ◽  
The Mean ◽  
Potential Remedy

Summary We consider the problem of segmented linear regression with a single breakpoint, with the focus on estimating the location of the breakpoint. If $n$ is the sample size, we show that the global minimax convergence rate for this problem in terms of the mean absolute error is $O(n^{-1/3})$. On the other hand, we demonstrate the construction of a super-efficient estimator that achieves the pointwise convergence rate of either $O(n^{-1})$ or $O(n^{-1/2})$ for every fixed parameter value, depending on whether the structural change is a jump or a kink. The implications of this example and a potential remedy are discussed.

scholarly journals Conjugate Gradient Hard Thresholding Pursuit Algorithm for Sparse Signal Recovery

Algorithms ◽  
2019 ◽  
Vol 12 (2) ◽  
pp. 36 ◽  
Author(s):  
Yanfeng Zhang ◽  
Yunbao Huang ◽  
Haiyan Li ◽  
Pu Li ◽  
Xi’an Fan
Keyword(s):  
Convergence Rate ◽  
Conjugate Gradient ◽  
Selection Strategy ◽  
Convergence Criterion ◽  
Signal Recovery ◽  
Hard Thresholding ◽  
Step Size ◽  
Iterative Hard Thresholding ◽  
Reconstruction Performance ◽  
Gaussian Signal

We propose a new iterative greedy algorithm to reconstruct sparse signals in Compressed Sensing. The algorithm, called Conjugate Gradient Hard Thresholding Pursuit (CGHTP), is a simple combination of Hard Thresholding Pursuit (HTP) and Conjugate Gradient Iterative Hard Thresholding (CGIHT). The conjugate gradient method with a fast asymptotic convergence rate is integrated into the HTP scheme that only uses simple line search, which accelerates the convergence of the iterative process. Moreover, an adaptive step size selection strategy, which constantly shrinks the step size until a convergence criterion is met, ensures that the algorithm has a stable and fast convergence rate without choosing step size. Finally, experiments on both Gaussian-signal and real-world images demonstrate the advantages of the proposed algorithm in convergence rate and reconstruction performance.

Localization of Intracellular Antigens in thin Sections with Ferritin Labeled Antibody

1970 ◽  
Vol 28 ◽  
pp. 174-175
Author(s):  
M.S. Shahrabadi ◽  
T. Yamamoto
Keyword(s):  
Bovine Serum Albumin ◽  
Bovine Serum ◽  
Antigenic Determinants ◽  
Conjugate Prior ◽  
Thin Sections ◽  
Specific Attachment ◽  
Intracellular Antigen ◽  
Antigen Antibody ◽  
Ideal Method ◽  
The Ideal

The technique of labeling of macromolecules with ferritin conjugated antibody has been successfully used for extracellular antigen by means of staining the specimen with conjugate prior to fixation and embedding. However, the ideal method to determine the location of intracellular antigen would be to do the antigen-antibody reaction in thin sections. This technique contains inherent problems such as the destruction of antigenic determinants during fixation or embedding and the non-specific attachment of conjugate to the embedding media. Certain embedding media such as polyampholytes (2) or cross-linked bovine serum albumin (3) have been introduced to overcome some of these problems.

Convergence of Finite Fifference Method for Parabolic Problem

2003 ◽  
Vol 3 (1) ◽  
pp. 45-58 ◽  
Author(s):  
Dejan Bojović
Keyword(s):  
Convergence Rate ◽  
Boundary Value Problem ◽  
Heat Equation ◽  
Parabolic Problem ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Variable Coefficients ◽  
Rate Estimate ◽  
Convergence Rate Estimate ◽  
Initial Boundary Value

Abstract In this paper we consider the first initial boundary-value problem for the heat equation with variable coefficients in a domain (0; 1)x(0; 1)x(0; T]. We assume that the solution of the problem and the coefficients of the equation belong to the corresponding anisotropic Sobolev spaces. Convergence rate estimate which is consistent with the smoothness of the data is obtained.

On the approximation of $ \ exp (-x) $ on the half-axis by spline functions in three-point rational interpolants

2019 ◽  
pp. 32-37
Author(s):  
Abdul-Rashid Ramazanov ◽  
V.G. Magomedova
Keyword(s):  
Convergence Rate ◽  
Spline Functions ◽  
Rational Spline ◽  
Rational Interpolants ◽  
Half Axis

For the function $f(x)=\exp(-x)$, $x\in [0,+\infty)$ on grids of nodes $\Delta: 0=x_0<x_1<\dots $ with $x_n\to +\infty$ we construct rational spline-functions such that $R_k(x,f, \Delta)=R_i(x,f)A_{i,k}(x)\linebreak+R_{i-1}(x, f)B_{i,k}(x)$ for $x\in[x_{i-1}, x_i]$ $(i=1,2,\dots)$ and $k=1,2,\dots$ Here $A_{i,k}(x)=(x-x_{i-1})^k/((x-x_{i-1})^k+(x_i-x)^k)$, $B_{i,k}(x)=1-A_{i,k}(x)$, $R_j(x,f)=\alpha_j+\beta_j(x-x_j)+\gamma_j/(x+1)$ $(j=1,2,\dots)$, $R_j(x_m,f)=f(x_m)$ при $m=j-1,j,j+1$; we take $R_0(x,f)\equiv R_1(x,f)$. Bounds for the convergence rate of $R_k(x,f, \Delta)$ with $f(x)=\exp(-x)$, $x\in [0,+\infty)$, are found.

Stability Analysis of the Nanjung Water Diversion Twin Tunnels based on Convergence Measurement

2019 ◽  
Vol 1 (1) ◽  
pp. 49-60
Author(s):  
Simon Heru Prassetyo ◽  
Ganda Marihot Simangunsong ◽  
Ridho Kresna Wattimena ◽  
Made Astawa Rai ◽  
Irwandy Arif ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Convergence Rate ◽  
Critical Strain ◽  
Convergence Rates ◽  
Strain Analysis ◽  
Water Diversion ◽  
Tunnel Face ◽  
Tunnel Stability ◽  
The Stability ◽  
Twin Tunnels

This paper focuses on the stability analysis of the Nanjung Water Diversion Twin Tunnels using convergence measurement. The Nanjung Tunnel is horseshoe-shaped in cross-section, 10.2 m x 9.2 m in dimension, and 230 m in length. The location of the tunnel is in Curug Jompong, Margaasih Subdistrict, Bandung. Convergence monitoring was done for 144 days between February 18 and July 11, 2019. The results of the convergence measurement were recorded and plotted into the curves of convergence vs. day and convergence vs. distance from tunnel face. From these plots, the continuity of the convergence and the convergence rate in the tunnel roof and wall were then analyzed. The convergence rates from each tunnel were also compared to empirical values to determine the level of tunnel stability. In general, the trend of convergence rate shows that the Nanjung Tunnel is stable without any indication of instability. Although there was a spike in the convergence rate at several STA in the measured span, that spike was not replicated by the convergence rate in the other measured spans and it was not continuous. The stability of the Nanjung Tunnel is also confirmed from the critical strain analysis, in which most of the STA measured have strain magnitudes located below the critical strain line and are less than 1%.

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