An alternative perspective on the mixture estimation problem

The paper presents an alternative perspective on the mixture estimation problem. First, observations are counted into a histogram. Secondly, rough and enhanced parameter estimation followed by the separation of observations is done. Finally, the residue is distributed between the components by the Bayes decision rule. The number of components, the mixture component parameters and the component weights are modelled jointly, no initial parameter estimates are required, the approach is numerically stable, the number of components has no influence upon the convergence and the speed of convergence is very high. The alternative perspective is compared to the EM algorithm and verified through several data sets. The presented algorithm showed significant advantages compared to the competitive methods and has already been successfully applied in reliability and fatigue analyses.     

混合高斯参数估计的动态簇算法

混合高斯概率密度模型可以很好地拟合非高斯样本的概率密度。在各高斯分量概率密度互不重叠的条件下,使用动态簇算法可以快速而精确地估计出混合高斯概率密度模型参数。这是一种基于最小均方差原则的递推算法,在正向推导出各种可能的簇边界后,再根据确定的最末边界值逆向推定各前导簇边界,从而得到混合高斯概率密度模型参数估计值。描述模型及参数估计问题之后,动态簇算法被推导出来。然后深入探讨了该算法的实质及适用条件。最后结合数值仿真实例,分析了动态簇算法的估计性能。     

Functions of singular random matrices with applications

This article describes how the Jacobian is found for certain functions of a singular random matrix, both in the general case and in that of a non-negative, definite random matrix. The Jacobian of the transformationV=S ² is found whenS is non-negative definite; in addition, the Jacobian of the transformationY=X ⁺ is determined whenX ⁺ is the generalized, or Moore-Penrose, inverse ofX. Expressions for the densities of the generalized inverse of the central beta and F singular random matrices are proposed. Finally, two applications in the field of Bayesian inference are presented. This work was supported in part by the research project 39017E of CONACYT-México This article was written during the first author's stay as a Visiting Professor in the Department of Statistics at the University of Granada, Spain     

考虑动态需求的生鲜商品物流配送优化方法研究

目的 针对生鲜商品配送过程中客户需求的变化,协调静态与动态客户需求之间的关系,合理规划路径,并降低物流总成本。方法 首先考虑客户生鲜需求的多样化温控区间、随机订单请求时间及动态需求量等因素,构建物流总成本最小化的整数规划模型。然后,设计基于高斯混合聚类的改进蚁群算法求解该模型,并提出动态需求处理策略,用于路径的再优化。其次,通过与粒子群算法、遗传算法和鲸鱼优化算法进行对比分析,验证文中设计算法的有效性。最后,以重庆市某生鲜配送网络为例,对比分析优化前后的运营指标,并探讨生鲜商品价值损失水平与物流总成本之间的关系。结果 经优化后,物流总成本下降了22.35%,其中惩罚成本、价值损失、配送成本和温控成本分别下降了39.84%、61.84%、29.80%、57.00%。结论 文中所提的模型、算法和动态需求处理策略可以合理规划配送路径,有效降低了总成本,为考虑动态需求的生鲜配送网络优化提供了参考。     

混合广义线性模型的统计推断

为了更好地拟合实际数据,本文提出了混合广义线性模型并进行参数估计．首先,基于异质总体的一阶矩以及二阶矩存在的条件下,运用混合广义线性模型对子总体的均值进行建模,构造扩展拟似然和伪似然函数,然后利用 EM 算法对均值参数、散度以及混合比例进行估计,并通过 Monte Carlo 模拟验证所提出的模型参数估计方法的有效性．最后,实例研究的结果表明本文的模型和方法是科学实用的．     

基于循环最大期望修正算法的与文本无关话者识别研究

话者识别中目标模型的最大期望算法存在着出现奇异阵的重大缺陷,而最大似然估计虽然不会出现奇异阵,但识别率比较低。提出了一种循环最大期望修正算法,采用最大似然估计所得模型为初始模型,然后用最大期望算法中每步的模型,通过α值控制修正比例对其进行修正。实验结果表明,该修正算法较好地克服了奇异阵的出现,同时提高了识别率。     

On the Likelihood Ratio Test for Compound Distributions for Homogeneity of Mixing Proportions

We consider the problem of comparing two multivariate compound distributions each with component densities f ₁, (x) and f ₂(x) and with mixing proportions p _x and (1 – p_x) for the first compound distribution and p_y and (1 – p_y ) for the second. The likelihood ratio test of the hypothesis H ₀: p_x = p_y is presented by using the EM algorithm to derive the maximum likelihood estimates. This test is applied to some actual data under the assumption that the underlying component densities are normal. The result is contrasted with results obtained using some existing univariate methods of testing H₀.     

基于遗传算法和有限混合分布的应力谱多模态建模

该文提出了一种基于遗传算法(genetic algorithm, GA)的有限混合分布参数估计方法, 应用该方法对青马大桥典型焊接节点的应力谱进行多模态建模。首先, 采用小波变换消除原始应变监测数据中的温度影响, 利用雨流计数法将应变时程曲线转化为日应力谱, 考虑到交通荷载(包括汽车荷载和火车荷载)和台风的影响, 建立标准日应力谱。然后, 采用三种不同的有限混合分布函数(有限混合正态分布函数、有限混合对数正态分布函数和有限混合威布尔分布函数)以及基于遗传算法的混合参数估计方法对应力幅进行多模态建模, 根据赤池信息准则(Akaike’s information criterion, AIC)确定最佳的有限混合模型。最后, 采用双变量有限混合分布和基于遗传算法的混合参数估计方法建立了应力幅和平均应力二维随机变量联合概率密度函数。结果表明, 该文提出的基于遗传算法的有限混合分布参数估计方法可以有效应用于二维随机变量的概率建模。     

A Statistical Physics Method of Electronic Device Reliability Testing from Working Data

A combined method is used to estimate the parameters for a mixture of exponential and Weibull distributions. Examples are given of the method applied in reliability analysis for high-power electronic devices.     

混合高斯参数估计的两种EM算法比较

混合高斯模型是一种典型的非高斯概率密度模型,获得广泛应用。其参数的优效估计可以通过最大似然方法获得,但最大似然估计往往因其非线性而难以实现,故期望最大化(Expectation-Maximization,EM)迭代算法成为一种常用的替代方法。常规EM算法性能受迭代初值设置影响大,且不能对模型阶数做出估计。一种名为贪婪EM的改进算法可以克服这两个缺点,获得更为准确的模型参数估计,但其运算量一般会远大于前者。本文对这两种EM算法进行综合研究,深入挖掘两者之间的关系,并基于相同的数值仿真实例,直观地演示比较两者的性能差异。     

The Measuring Process

This paper deals with the theory of a proposed method for the statistical study of measuring processes. The practical aspects of the method, including computational details, are discussed in a companion paper published in the ASTM Bulletin. In the present article a theoretical framework is proposed for the mathematical expression of the sources of variation in measuring methods and a suitable method of statistical analysis is described. Particular attention is given, both here and in the companion paper, to interlaboratory studies of test methods. An illustration based on data taken from the chemical literature is appended.