Implicit Sampling, with Application to Data Assimilation

There are many computational tasks, in which it is necessary to sample a given probability density function (or pdf for short), i.e., to use a computer to construct a sequence of independent random vectors x i (i = 1, 2, ··· ), whose histogram converges to the given pdf. This can be difficult because the sample space can be huge, and more importantly, because the portion of the space, where the density is significant, can be very small, so that one may miss it by an ill-designed sampling scheme. Indeed, Markovchain Monte Carlo, the most widely used sampling scheme, can be thought of as a search algorithm, where one starts at an arbitrary point and one advances step-by-step towards the high probability region of the space. This can be expensive, in particular because one is typically interested in independent samples, while the chain has a memory. The authors present an alternative, in which samples are found by solving an algebraic equation with a random right-hand side rather than by following a chain; each sample is independent of the previous samples. The construction in the context of numerical integration is explained, and then it is applied to data assimilation.     

Spectral Analysis of Model Couette Flows in Application to the Ocean

Computational Mathematics and Mathematical Physics - A method for analysis of the evolution equation of potential vorticity in the quasi-geostrophic approximation with allowance for vertical...     

一种区间数的因子分析技术及其在证券市场中的应用

传统的因子分析技术能够有效地对高维变量空间进行降维处理,但它对于样本空间却缺乏行之有效的降维效果.为了解决这一问题,一种针对大量样本数据、新的因子分析技术———区间数因子分析技术(intervaldatafactoranalysis,IFA)被提出并得到了迅速的发展。IFA方法对传统的数据概念做了本质性的扩张,运用'数据打包'的理念,对海量原始数据在不破坏其原有内在逻辑关系的前提下,可以进行变量和样本点维度的双重降维。本文详细阐述了区间数因子分析技术的原理,并以中国股票市场为案例研究背景,结果表明IFA分析技术对大规模多维数据系统做综合简化是十分有效的。     

反应扩散系统的上三角阵法

本文介绍反应扩散系统的上三角阵方法,并讨论一个典型的模型.     

多指标面板数据因子分析的分层模型及应用

针对多指标面板数据的公因子提取及评价问题,提出一种充分挖掘面板数据时间序列价值的分层因子模型.模型在底层上通过对各个时点上截面数据指标变量的精炼实现对截面样本数据的评价,将截面数据压缩成只具有时间维度的样本评价值向量;模型顶层进一步实现了对由各个截面样本评价值向量形成的综合评价矩阵时间维度的精炼,并推导出面板数据因子得分公式及评价函数.最后,运用模型方法对我国大陆31个省市国有及规模以上非国有企业生产及经营状态面板数据进行了因子分析,分析结果显示了方法的合理性.分层模型实现了对面板数据各样本的指标维度与时间维度的双重提炼,弥补了现有方法的片面性与局限性.     

Copula函数的选择：方法与应用

针对目前Copula函数在实际应用中的选择问题,本文通过非参数法得到了它们的分布函数图及其经验分布图并进行了比较,然后利用一种解析法对其进一步的选择,并通过Q-Q图比较了各种模型的拟合程度,最后进行了拟合优度检验,得到了最优的Copula。最后对国内的上证A股指数和上证B股指数进行了实证分析,结果体现了该方法的有效性。     

数据同化中的伴随方法的有关问题的研究

关于伴随方法应用中只能利用模式的伴随的观点,被认为是有疑问的．所作的数值模拟实验表明,对于潮波模型而言,方程的伴随能够得到与模式的伴随同样的结果:调和常数的实测值与模拟值的振幅差的绝对值的平均小于5.0 cm,迟角差的绝对值的平均小于5.0°．这些结果都能够体现渤、黄海M2分潮的基本特征．作为对比,也利用前人的方法对渤、黄海的M2分潮潮波进行了数值模拟,首先借助于历史资料和观测资料得到开边界的初始猜测,然后对开边界的初始猜测值进行调整,以得到与高度计资料之差尽可能小的模拟结果．但由于开边界的值共有72个,究竟有哪些值需要调整,需要如何调整,只有经过不断的调试,才能部分地解决这些问题．工作量大且很难得到令人满意的结果．该文实现了确定开边界条件的自动化过程,这与前人的方法相比,有无可比拟的优势．需要特别强调的是如果利用方程的伴随,可以避免繁琐而冗长的数学推导．因而说明方程的伴随也应该引起足够的重视．     

动态数据拟合的叠合模型及其应用

对复杂现象的动态序列建模，一般单一模型效果不是太好，本给出叠合模型的建模方法，着重讨论周期性趋势的叠合模型方法，并对其作了改进。章利用改进的周期性趋势叠合模型对我国非典型肺炎临床诊断病人数作出了非常满意的拟合。     

火场-结构联合分析简化模型及其应用研究

为在建筑结构火灾反应分析中考虑实际火场特性,并简化火场分析模型与结构有限元分析模型之间的复杂对应关系,提出并建立了火场温度及对流辐射边界的热传导分析时空模型(STM)和基于时空模型的火场-结构联合分析方法。该方法根据火场模型计算出室内火场温度分布场以及对流辐射边界场离散数据,通过双向正交多项式进行拟合来得到不同时刻的构件边界连续时空模型,再通过时空模型进行热传导分析和热力耦合分析,从而实现火场-结构联合分析方法。在验证其合理性的基础上,通过ABAQUS子程序UTEMP和DFLUX实现其分析过程,并进行了北京某档案馆工程的应用分析,结果表明该方法可以较好地联合火场模拟与结构分析用于结构火灾安全评价。     

有终端控制的随机模型及其应用

本文目的是建立在以工作年限为终端的控制下预测个人未来发展的随机模型．调查的主体是济南市市民,其中个人发展简化由个人月收入代替衡量．首先在大学生之中进行一个调查确定对个人发展影响较为明显的几个因素作为目标因素,然后根据结果制定新的调查问卷在已工作人士中展开,分类统计不同工作年限的被调查人所填写的调查问卷,根据结果统计应用EVIEWS等软件建立随机模型．     

Two Approaches to Scheduling Container Ships with an Application to the North Atlantic Route

The development of an interactive computer program and a heuristic optimising model for scheduling container ships on the North Atlantic is described. The constraints and multiple objective criteria governing these schedules are discussed and sample results of both approaches given.     

一种估计Logistic模型参数的方法及应用实例

分析了Logistic函数的解析性质,得到了曲线上三个关键点和三个不同的增长阶段,利用差分和最小二乘法,给出了Logistic模型的一种便于使用的参数估计方法．并通过实例,建立Logistic模型对我国城镇居民家庭平均每百户彩色电视机拥有量的增长变化趋势进行了分析和预测．     

Stochastic Model of an Intermittently Used System with Non-perpetual Vigil: Its Estimation Study

Abstract

A two-unit intermittently used standby system when it is not under perpetual vigil is studied. Our interest centers on Bayesian estimation of stationary rate of disappointments, assuming an informative prior for the unknown parameters in the model. Gibbs sampling is used to derive the posterior distribution of the stationary rate of disappointments and subsequently the highest posterior density (HPD) intervals. A simulation study illustrates the results.     

滑动数据重心预测方法及其应用研究

本文在研究多因素数据重心法的基础上,进一步提出滑动数据重心预测方法,该方法是对原始样本数据提出了一种新的数据处理方法,大大降低了由于历史数据组中的异常点对预测结果产生的破坏性。通过建立我国钢材消费量与国内生产总值(GDP)的计量动态模型对该方法与多因素数据重心预测法进行对比研究。同时利用时间序列自回归AR(p)对计量动态模型的初级预测结果进行差值校正,并将该方法应用于我国2015年、2020年的钢材消费量预测。对比研究表明该方法使得预测结果更加精确、稳健。     

多指标面板数据聚类方法及应用——以行业一次能源消费面板数据为例

综合考虑面板数据多指标中因变量指标特征及其与自变量指标的相关关系,通过定义因变量自协方差及自变量与因变量协方差以构建面板数据相似及相关性测度距离函数,在引入自组织竞争网络算法的基础之上,提出了多指标面板数据聚类的方法.以我国1996-2008年44个行业煤炭、天然气、电力消耗量及国际石油价格面板数据进行实际应用,验证了新方法聚类结果更为显著的优点。     

基于数据流形结构的聚类方法及其应用研究

随着信息社会的不断发展,人类已经进入了信息爆炸时代,海量的数据使数据处理变得繁琐复杂,因此如何对现有的高维数据降维、聚类,并在一定程度上消除高维数据中存在的噪声是解决该问题的关键.基于相关的理论知识采用先降维后聚类的步骤,把高维数据按照子空间结构和流形结构两种情况分类,运用稀疏子空间聚类、谱多流形聚类、K-manifolds方法进行建模求解,通过对各种方法的对比,得出谱多流形聚类方法运行速度快,聚类准确度高,是最具有一般性特征的模型.     

A Stochastic Approximation Method and Its Application to Confidence Intervals

The oldest stochastic approximation method is the Robbins–Monro process. This estimates an unknown scalar parameter by stepping from one trial value for the parameter to another, adopting the last trial value as the estimate. More recent research suggests there are benefits from taking larger steps than with the Robbins–Monro process and then obtaining an estimate by averaging the later trial values. Work on the averaged estimator has made only general assumptions and here we consider a more explicit case that is of practical importance. Stronger asymptotic results are developed and simulations show they hold well for moderately long searches. The results motivate the development of a new method of searching for the endpoints of a confidence interval. This method performs decidedly better than a previously proposed method in terms of both the position of endpoints and the coverage of confidence intervals. The efficiency of the new method is typically well in excess of 90%.

Computer code and an appendix containing the derivation of asymptotic efficiencies are available in the online supplements.     

PBDW: A non-intrusive Reduced Basis Data Assimilation method and its application to an urban dispersion modeling framework

The challenges of understanding the impacts of air pollution require detailed information on the state of air quality. While many modeling approaches attempt to treat this problem, physically-based deterministic methods are often overlooked due to their costly computational requirements and complicated implementation. In this work we extend a non-intrusive Reduced Basis Data Assimilation method (known as PBDW state estimation) to large pollutant dispersion case studies relying on equations involved in chemical transport models for air quality modeling. This, with the goal of rendering methods based on parameterized partial differential equations (PDE) feasible in air quality modeling applications requiring quasi-real-time approximation and correction of model error in imperfect models. Reduced basis methods (RBM) aim to compute a cheap and accurate approximation of a physical state using approximation spaces made of a suitable sample of solutions to the model. One of the keys of these techniques is the decomposition of the computational work into an expensive one-time offline stage and a low-cost parameter-dependent online stage. Traditional RBMs require modifying the assembly routines of the computational code, an intrusive procedure which may be impossible in cases of operational model codes. We propose a less intrusive reduced order method using data assimilation for measured pollution concentrations, adapted for consideration of the scale and specific application to exterior pollutant dispersion as can be found in urban air quality studies. Common statistical techniques of data assimilation in use in these applications require large historical data sets, or time-consuming iterative methods. The method proposed here avoids both disadvantages. In the case studies presented in this work, the method allows to correct for unmodeled physics and treat cases of unknown parameter values, all while significantly reducing online computational time.