用导数求极值的方法提高病毒检测的效率

在进行大规模新冠检测时,我国采用先对样本分组、再将样本混合检测的策略取得了很好的检测效率.但是在对样本进行分组时,单组的样本数量选择多少是最好呢?我们对此问题进行了数学建模分析:以降低总检测次数为优化目标,找出总检测次数与单组样本数量之间的函数关系,采用导数求极值的计算方法,获得了最优的单组样本数量取值.     

单纯随机抽样理论之我见

针对一般经济统计教材中普遍存在的关于单纯随机抽样过程中,不同抽样方法下样本方差的无偏性问题提出自己的见解.认为,抽样理论源于实践,重复抽样时有Nn个样本、不重复抽样时有CnN个样本是实际抽样调查工作中普遍采用的方式、方法,更是单纯随机抽样推断理论的源泉.在此基础上数学界将实际工作中各种可能始点的抽样方法赋予理性思考、研究,获得结论:无限制抽样和简单随机抽样条件下样本方差是总体方差的无偏估计量.     

PPS适应性整群抽样下估计量的研究

在群规模存在差异时,最有效的抽样方法是PPS整群抽样;在单元存在聚集性且总体信息不明确时,使用PPS适应性整群抽样是最有效的.利用PPS适应性整群抽样设计中的样本外推机制产生的样本信息,对HH和HT估计进行调整,提出修正的HH和HT估计,并对估计量的性质进行了研究.     

多目标调查的MPPS平衡抽样方法研究

平衡抽样是广受关注的利用辅助信息改善样本结构的抽样方法.MPPS抽样在多目标调查中采用的与多变量规模成比例的入样概率,可以在平衡抽样中精确满足.基于MPPS抽样和平衡抽样的性质,文章提出多目标调查下的MPPS平衡抽样,该方法主要思想是将多个调查变量的辅助信息在确定入样概率和随机抽样过程中同时使用,提高HT估计量精度.模...     

国家标准GB2828的评介

一、概述 在国标GB2828颁布之前,我国广泛使用的抽样方法是百分比抽样方法.百分比抽样方法不但落后,而且在原理上是错误的,国际上早就不用了.GB2828的颁布执行,标志着我国抽样方法的一大进步. 对交验批进行质量验收,通常有两种方法,全数检验和抽样检验. 全数检验是对一批产品中的每一件产品逐个进行检验.由于有时检验方法具有破坏性或批量大,检验项目多,检验比较费时又费力,致使全数检验不可能或者不经济. 抽样检验是按统计方法,从一批交验的产品中随机抽取适量的产品进行检验,把检验结果与判定标准进行比较,从而确定该批产品是否合格. 在…     

基于平衡样本的校准估计研究--以规模以下工业企业测算为例

为解决规模以下工业企业调查中存在的样本代表性不足的问题,提出基于平衡样本的校准估计方法,并得出相应的估计量和估计量方差。该方法在抽样设计阶段采用了平衡抽样设计,在估计阶段采用了校准估计方法,较大限度地使用了辅助信息;通过数据分析得出基于平衡样本的校准估计方法要优于基于平衡抽样的HT估计方法。同时,为满足平衡变量间线性无关的假定,提出使用主成分分析、切片逆回归和切片平均方差估计三种方法对相关的平衡变量进行处理的思路。该方法对我国规模以下工业企业调查的完善具有理论与实践的双重意义,可适当的推广至我国政府统计的其他调查中。     

钢管再生混凝土柱承载力计算对比及可靠度分析

基于钢管再生混凝土轴压构件承载力的试验结果与采用各国规程的计算结果的对比分析,从统计意义上表明方钢管再生混凝土构件用DBJ13-51-2003规程的计算结果与试验结果吻合较好,圆钢管再生混凝土构件用DL/T5085-1999规程较好.并利用改进一次二阶矩法(JC法)对钢管再生混凝土轴压构件的极限承载力进行了可靠度分析,分析结果表明:钢管再生混凝土构件承载力的可靠度指标随荷载组合和荷载效应比的变化而变化,随再生混凝土强度等级的提高而增大,钢管壁厚、再生骨料取代率对可靠指标无明显影响.     

基于向量值有理插值的最优预测算法研究及陶瓷需求量预测的应用

通过对高维数据整体表达式建模预测方法和分区间等预测算法的缺陷分析,提出基于向量值有理插值的最优预测算法,通过有理向量插值函数和各分量的误差限得到向量之间的相似性,克服了其它很多算法利用向量的整体表达式方法而产生预测的偏差;另外,通过向量的误差限与训练样本所得向量值有理插值函数及迭代仿真方法来确定预测样本向量所对应的最优预测值.通过实例,算法所得预测值的精度比其他算法更高,并且分析了误差限和迭代步长对算法性能的影响.     

代表点数目对概率密度演化方法分析精度的影响

基于物理随机地震动模型和切球选点法生成3组不同容量地震动样本,以此作为外激励输入,采用概率密度演化方法分别对结构进行随机地震反应分析,并对分析结果进行比较,以研究代表点数目对分析精度的影响.数值分析结果表明,基于切球选点法生成的少量代表样本能够对目标总体的一、二阶统计特性进行较为准确地估计;当样本容量较小时,结构随机动力响应在各时刻的概率分布分析结果具有一定的误差.因此,应根据随机动力系统中随机变量的数目、所采用的选点方法以及预期的计算精度合理确定概率密度演化方法中样本的容量.     

基于因变量抽样设计下线性回归模型的假设检验问题

在许多大型队列研究中,采用节约成本并能提高效率的抽样机制至关重要,基于因变量的抽样设计正是这样一种有偏抽样机制.这种方法最大的优点在于:能够将资源集中在那些包含有更多的协变量与因变量关系信息的研究群体上.本文研究基于因变量抽样设计下的线性模型中回归方程显著性检验以及回归系数显著性检验问题.基于一种半参数经验轮廓似然的方法,我们分别为回归方程检验与回归系数检验提出了相应的检验统计量,获得了所提出检验统计量的渐近性质.通过模拟研究评估了所提出的检验方法在有限样本下的表现,并应用提出的方法分析了一个孕妇分娩的实际数据.     

一种满足有效样本量固定的放回抽样方法

相比不放回抽样,放回抽样的实施比较简单,操作性强,但缺点在于单元可能被重复抽到,抽出的有效样本量小于等于样本量,不是固定的。本文应用逆抽样的原理,设计了一种放回抽样方法,满足有效样本量固定,并且估计量的性质优良。     

Random sampling within the framework of a multivariate principal-agent approach

In this paper, we analyze a specific class of principal-agent models which seems to be sufficiently general to cover applications in environmental economics with upstream-downstream problems as an example. In our basic model, the observation outcome is ann-dimensional random vectorx and only the first and second moments ofx are common knowledge. We study the effects of random sampling in the presence of costly signals. For this purpose, we assume that the principal and the agent use a simple statistical procedure, i.e. their contract will be based on the mean of a random sample with sampling costs dependent on the sample size. It is shown that there exists an optimal sample size. We investigate the relationship between the optimal sample size, the marginal sampling costs, and the agent's risk aversion.     

定时截尾下指数分布产品可靠性抽样检验方案

本文给出了制订定时截尾下指数分布产品可靠性抽样检验方案的统计方法.检验统计量是平均寿命倒数的极大似然估计.提出了一种选择截尾时间的方法.利用分布分位数的Cornish-Fisher展开近似地确定了样本量和接收常数.模拟结果表明,本文给出的方法是可行的.     

基于有序抽样样本的参数的极大似然估计的性质

有序抽样是一种新的抽样方法 ,与简单随机抽样方法相比它具有很多很好的性质 .本文讨论了在有序抽样样本下的参数的极大似然估计的性质 .     

Empirical Likelihood Inference Under Stratified Random Sampling in the Presence of Measurement Error

Suppose that several different imperfect instruments and one perfect instrument are used independently to measure some characteristic of a population. In order to make full use of the sample information, in this paper the empirical likelihood method is put forward for making inferences on parameters of interest under stratified random sampling in the presence of measurement error, Our results show that it can lead to estimators which are asymptotically normal and utilize all the available sample information. We also obtain the asymptotic distribution of empirical likelihood testing statistics. In particular, we apply the method to obtain estimator and confidence interval of population mean.     

Implementations of the Monte Carlo EM Algorithm

The Monte Carlo EM (MCEM) algorithm is a modification of the EM algorithm where the expectation in the E-step is computed numerically through Monte Carlo simulations. The most exible and generally applicable approach to obtaining a Monte Carlo sample in each iteration of an MCEM algorithm is through Markov chain Monte Carlo (MCMC) routines such as the Gibbs and Metropolis–Hastings samplers. Although MCMC estimation presents a tractable solution to problems where the E-step is not available in closed form, two issues arise when implementing this MCEM routine: (1) how do we minimize the computational cost in obtaining an MCMC sample? and (2) how do we choose the Monte Carlo sample size? We address the first question through an application of importance sampling whereby samples drawn during previous EM iterations are recycled rather than running an MCMC sampler each MCEM iteration. The second question is addressed through an application of regenerative simulation. We obtain approximate independent and identical samples by subsampling the generated MCMC sample during different renewal periods. Standard central limit theorems may thus be used to gauge Monte Carlo error. In particular, we apply an automated rule for increasing the Monte Carlo sample size when the Monte Carlo error overwhelms the EM estimate at any given iteration. We illustrate our MCEM algorithm through analyses of two datasets fit by generalized linear mixed models. As a part of these applications, we demonstrate the improvement in computational cost and efficiency of our routine over alternative MCEM strategies.     

Optimization approach to the design of frequency sampling filters

Many digital signal processing applications require linear phase filtering. For applications that require narrow-band linear phase filtering, frequency sampling filters can implement linear phase filters more efficiently than the commonly used direct convolution filter. In this paper, a technique is developed for designing linear phase frequency sampling filters. A frequency sampling filter approximates a desired frequency response by interpolating a frequency response through a set of frequency samples taken from the desired frequency response. Although the frequency response of a frequency sampling filter passes through the frequency samples, the frequency response may not be well behaved between the specific samples. Linear programming is commonly used to control the interpolation errors between frequency samples. The design method developed in this paper controls the interpolation errors between frequency samples by minimizing the mean square error between the desired and actual frequency responses in the stopband and passband. This design method describes the frequency sampling filter design problem as a constrained optimization problem which is solved using the Lagrange multiplier optimization method. This results in a set of linear equations which when solved determine the filter's coefficients.This work was partially funded by The National Supercomputing Center for Energy and the Environment, University of Nevada Las Vegas, Las Vegas, Nevada and by NSF Grant MIP-9200581.     

On when to stop sampling for the maximum

Suppose a sequential sample is taken from an unknown discrete probability distribution on an unknown range of integers, in an effort to sample its maximum. A crucial issue is an appropriate stopping rude determining when to terminate the sampling process. We approach this problem from a Bayesian perspective, and derive stopping rules that minimize loss functions which assign a loss to the sample size and to the deviation between the maximum in the sample and the true (unknown) maximum. We will show that our rules offer an extremely simple approximate solution to the well-known problem to terminate the Multistart method for continuous global optimization.     

(对数)逻辑斯谛克分布下可靠性抽样检验

对于寿命遵从逻辑斯谛克分布或对数逻辑斯谛克分布的产品,本文在完全样本情形给出了制定可靠性抽样检验方案的统计方法.数值模拟结果表明该方法是可行的.本文还指出,这种方法可用于位置一刻度参数分布族.     

你也需要蒙特卡罗方法——提高应用水平的若干技巧

本文是《你也需要蒙特卡罗方法》中的第二篇。文中讨论提高应用水平的一些技巧,涉及模拟模型的选取,提高计算速度或降低抽样方差的一些方法,诸如重要抽样、相关抽样、对偶抽样和分层抽样等。还讨论了模拟中所需的抽样次数的确定和模拟结果的精度评估等实用问题。