删失截断情形下失效率变点模型的Bayes参数估计

通过添加部分缺失寿命变量数据,得到了删失截断情形下失效率变点模型相对简单的似然函数.讨论了所添加缺失数据变量的概率分布和随机抽样方法.利用Monte Carlo EM算法对未知参数进行了迭代.结合Metropolis-Hastings算法对参数的满条件分布进行了Gibbs抽样,基于Gibbs样本对参数进行估计,详细介绍了MCMC方法的实施步骤.随机模拟试验的结果表明各参数Bayes估计的精度较高.     

截断删失情形下泊松分布参数多变点的Bayes估计

通过添加数据得到截断删失情形下泊松分布的完全数据似然函数,研究变点位置和其它参数的满条件分布.利用Gibbs抽样与Metropolis-Hastings算法相结合的MCMC方法对参数进行估计,详细介绍MCMC方法的实施步骤.随机模拟试验的结果表明参数Bayes估计的精度较高.     

IIRCT下泊松分布参数多变点模型的贝叶斯估计

通过添加缺损的寿命变量数据得到了带有不完全信息随机截尾试验下泊松分布参数多变点模型的完全数据似然函数,研究了变点位置参数和其它参数的满条件分布.利用Gibbs抽样与Metropolis-Hastings算法相结合的MCMC方法对各参数的满条件分布分别进行了抽样,把Gibbs样本的均值作为各参数的贝叶斯估计,并且详细介绍了MCMC方法的实施步骤.最后进行了随机模拟试验,试验结果表明各参数贝叶斯估计的精度都较高.     

屏蔽数据下指数分布两部件串联系统多变点模型的贝叶斯估计

通过引入潜在变量得到了截尾情形屏蔽数据下指数分布两部件串联系统交点模型较简单的似然函数.利用Gibbs抽样与Metropolis-Hastings算法相结合的MCMC方法对各参数进行了抽样.基于Gibbs样本对参数进行估计.随机模拟的结果表明估计的精度较高.     

软件可靠性模型的Bayes推断及Gibbs算法

作为重要的软件可靠性模型,JM模型的研究具有重要意义.论文研究了JM模型Bayes估计及其Gibbs算法.在先验分布确定的情况下,给出了Bayes估计的Gibbs算法,并证明了其收敛性.最后通过模拟分析发现：在1≥100,k〉600时,所得到的参数Bayes估计与初始值几乎无关.从而说明Gibbs算法的可行性.     

基于MCMC模拟方法的带变点的NHPP软件可靠性模型

本文主要讨论软件测试过程中NHPP模型参数发生变化的情形,并用Bayes方法对GGO模型进行变点分析,运用基于Gibbs抽样的MCMC方法模拟出参数后验分布的马尔科夫链,最后借助于BUGS软件包对软件故障数据集Musa进行建模仿真,其结果表明该模型在软件可靠性变点分析中的直观性和有效性。     

左截断右删失数据下离散型寿命失效率变点模型的Bayes参数估计

利用EM算法和MCMC方法得到了左截断右删失数据下离散型寿命失效率变点模型的参数估计.利用筛选法对缺失数据进行填充,对各参数进行Gibbs抽样.随机模拟证实方法可行且参数估计的精度较高.     

NMAR机制下非线性均值方差模型的Bayes估计

讨论响应变量带有不可忽略缺失数据的非线性均值方差模型的Bayes估计问题.缺失数据机制由logistic回归模型来指定,运用Gibbs抽样及MH算法得到模型参数和缺失数据机制参数的联合Bayes估计,模拟研究和实例分析展示上述模型和方法的可行性.     

三参数Weibull分布参数的Bayes估计

给出了三参数Weibull分布参数Bayes估计的两种方法,其一基于Laplace数值积分法,其二基于Gibbs抽样方法.模拟例子说明了估计方法的有效性.     

指数分布场合恒加试验缺失数据的Bayes统计分析

主要讨论了当寿命分布是指数分布时恒定应力加速寿命试验中常见几类数据类型(完全样本,分组样本,删失样本)的Bayes统计分析方法.运用G ibbs抽样迭代算法成功解决了Bayes分析中极为复杂的后验边际分布的计算问题,得到了满足顺序约束的参数的Bayes估计.模拟结果表明各场合下此方法均较好.     

Qualitative Analysis of Bifurcating Solutions in the Lengyel-Epstein Model

One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the＇living world. In his seminal paper ＂The Chemical Basis of Morphogenesis＂, Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates（1990） on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing＇s prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction-diffusion equations. The Lengyel-Epstein model is in the form as follows     

(0,1 ;0)-INTERPOLATION ON INFINITE INTERVAL (-∞, +∞)

In this paper, we study the explicit representation and convergence of (0, 1; 0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤ 3n - 2 when the function values are prescribed at two set of points namely the zeros of Hn(x) and H′n(x) and the first derivatives at the zeros of H′n(x).     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

Journal of the Operations Research Society of China Special issue on Operations Research in Healthcare Management

正Guest Editors:Hong Chen,Shanghai Jiao Tong University,Shanghai,China Guohua Wan,Shanghai Jiao Tong University,Shanghai,China David Yao,Columbia University,New York,USA Scope:Healthcare delivery worldwide has been fraught with high cost,low efficiency and poor quality of patient care service.For the field of operations research(OR),healthcare offers some of the biggest challenges as well as best opportunities in     

ANALYSIS IN THEORY AND APPLICATIONS Vol. 30, 2014 CONTENTS

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On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

An alternative mathematical algorithm for the photo- and videokeratoscope

Due to the resolution of current laser technology, the accuracy of corneal topography as measured by the videokeratoscope is no longer adequate to provide precise enough data for refractive surgery or for the fitting of customized contact lenses. We present an algorithm for recovering corneal topography that makes use of modern differential geometric techniques and numerical descent in Sobolev spaces. We believe this algorithm may be used with the photo- and videokeratoscope to increase the accuracy of the recovered corneal topography.