0-1序列中变点的贝叶斯分析

对于0-1(伯努利)序列中的变点问题,本文提出了一个确定变点的个数和位置的贝叶斯方法。首先借助于二分法把变点个数的确定问题转化为一系列对没有变点和仅有一个变点的模型进行比较的问题,然后通过贝叶斯因子进行模型比较。本文得到了贝叶斯因子和未知变点的后验分布的显式表达式。最后,通过对上证指数数据的实证分析阐释了所提方法的有效性。     

正态分布方差变点的检验

本文讨论了正态分布方差只有一个变点的检验问题，我们构造了三个检验统计量，其中L检验基于非参数U统计量，B检验基于Bayes方法，R检验由极大似然比方法导出．本文给出了L、B、R检验的渐近临界值，并用MonteCarlo模拟方法研究了这三个检验与平方的CUSUM检验以及LM检验的势，并进行了比较。当变点在序列的前一半位置时，L和R检验较好，当变点在序列的后一半位置时，平方的CUSUM和B检验较好．     

基于黄金分割法的离散回归方程的变点估计及其应用

本文利用变点统计学和黄金分割法讨论有多个变点的离散回归方程的交点估计和参数估计，文中提出基于黄金分割法搜索最佳变点估计和同时得到参数估计的最小二乘算法，还讨论该算法在控制领域的应用，数值模拟结果显示本文算法能给出良好的变点及参数的估计值。     

基于SaRa的面板数据回归模型结构变点估计

面板数据的变点分析是计量经济学的热门研究课题之一,在金融、医学、质量控制、气象等领域也有着广泛的应用.基于一种快速局部算法SaRa (Screening and Ranking algorithm)研究了面板数据回归模型的结构变点估计问题.首先基于回归系数的估计量建立局部统计量,筛选出可能的变点.其次构造自适应阈值来筛选出最终的变点,并且证明了变点估计量的一致性.Monte Carlo模拟结果显示,当解释变量为外生变量或内生变量,误差项存在序列相关或异方差,提出的方法都能较准确地估计出变点的个数及位置.最后利用该方法分析世界24个低收入和高收入国家自然人口增长率和国际移民存量对人口增长率的影响,说明了方法的有效性.     

基于非参数方法的交通流变点问题分析

考虑到交通流数据的分布形式不确定及其变点数目未知的实际情形,以基于非参数方法的交通流变点问题为研究对象,拟通过基于Kolmogorov-Smirnov(KS)检验和Mann-Whitney U检验的滑动窗口法实现变点存在与否的检验,进一步结合二分法对交通流数据变点数目及其位置进行估计.正态分布模拟仿真显示,两种方法对于均值变点检验和估计效果较好,而对于方差变点检验和估计,Mann-Whitney U方法不及K-S方法.最后,贵阳市中心道路车流量数据实例分析,表明方法对于交通流突变分析效果较好,可为相关部门提供可靠的决策依据.     

短样本多指标动态经济数据变点的一种识别方法

本文研究了多指标动态经济数据的变点问题,使用多元分析的方法,给出了在样本长度较短情况下识别变点的一种方法,并用这种方法分析了国民经济统计中的一个实际例子。     

论医学数学化

回顾科学发展的历史，特别是自然科学，如物理学、天文学等，都把数学作为自己学科的基础和工具，首先将物理问题用数学作定量描述，利用数学方法计算推导建立模型，经过实践检验，求得新的理论，使物理学的研究从定性的，描述性的水平，通过数学引向定量的、精确的高水平。科学研究的这条数学化的途径，基本上适用于一切科学。它的一般模式是： “实际→数学化（定量分析）→数学模型→检验→应用。”这是一种先进的、科学研究方法，不仅可以使某些实际问题典型化、数量化，有利于问题的解决，而且在建立模型的过程中增强了数学的生命力。…     

线性常微分方程参数稳定性的统计推断

对具有随机误差的观测数据, 讨论了常系数线性常微分方程参数稳定性的统计推断问题. 通过残差项的Karhunen-Loeve 分解, 给出了变点检验步骤及其在原假设下的极限分布. 在对立假设下定义了变点的估计, 证明了检验以及估计的一致性. 对常系数二阶常微分方程进行了统计模拟, 结果表明原假设下的极限分布是对真实分布非常好的近似; 对立假设下, 即使输入函数的频率存在0.75% 的变化, 上述检验也能以大概率拒绝原假设. 最后利用上述方法研究了英国中部地区的气温数据, 揭示了数据一些新的特点.     

基于Weibull分布的最大风速变点估计

利用三参数的Weibull分布分析安徽砀山气象站年最大风速数据,建立似然比变点模型和回归变点模型,并对年最大风速序列的变点进行检验和估计.考虑非气象因素对年最大风速序列的影响,选取A气象站附近数个气象站的年最大风速序列作为参考序列,通过比值法,消除气象因素的影响.计算结果表明,由似然比变点模型可以估计出A气象站最大风速变点出现在2003年,由回归变点模型估计出的变点出现在2009年和2003年.结合安徽砀山气象站实际迁移和海拔变化的历史沿革,可以发现,基于Weibull分布的变点模型成功检测出了2009年台站迁移和2003年前后台站迁移且海拔显著变化的情况.     

潜周期模型中频率变点的估计

本文用逐段计算周期图的办法研究了带有频率交点的潜周期模型估计问题，给出了交点数目、位置和潜频率的强相合估计．数值模拟表明本文方法对变点个数和潜频率估计很好，但是要准确估计交点位置需要较大样本量，估计对于噪声水平较高情况仍然有效。     

基于自适应延时神经网络的短时交通流预测

为了提高交通流诱导系统的性能,研究了一种基于自适应延时神经网络算法的短时交通流量预测模型,该算法与传统的神经网络方法相比在神经网络的结构和神经网络的训练方法两个方面进行了改进,更适用于预测具有不确定性、非线性、动态性等特征的短时交通流,同时用Matlab7.0编写程序对算法进行了仿真实现,根据仿真结果的分析验证了算法时实性和精确性.     

QoS-Guided Bandwidth Management in Differentiated Time Scales

This paper presents an integrated approach to QoS-guided network bandwidth allocation where each traffic flow requires a sufficient bandwidth allocation to support its mean traffic rate and to meet a delay requirement. Under the assumption that the peak rate of each traffic flow is decreasing with the time interval within which the rate is measured, we derive an analytical relationship between the delay bound and the bandwidth requirement for each individual flow. Then, based on a Gaussian aggregate traffic model, we show that two key controllable parameters, the coefficient of variation and the provision for variation for the aggregate traffic flow, determine all three fundamental QoS attributes (throughput, delay, and loss). We illustrate by examples that these results can be used to design admission policies. We demonstrate also quantitatively a remarkable QoS advantage of larger channel bandwidth in a statistical multiplexing environment. The analytical contributions are expected to be generally useful in QoS-guided bandwidth management in broadband networks.     

Analysis of traffic flow by the finite element method

A finite elernent methodology is developed for the numerical solution of traffic flow problems encountered in arterial streets. The simple continuum traffic flow model consisting of the equation of continuity and an equilibrium flow-density relationship is adopted. A Galerkin type finite element method is used to formulate the problem in discrete form and the solution is obtained by a step-by-step time integration in conjunction with the Newton-Raphson method. The proposed finite element methodology, which is of the shock capturing type, is applied to flow traffic problems. Two numerical examples illustrate the method and demonstrate its advantages over other analytical or numerical techniques.     

Analytical studies on the instabilities of heterogeneous intelligent traffic flow

It has been widely reported in literature that a small perturbation in traffic flow such as a sudden deceleration of a vehicle could lead to the formation of traffic jams without a clear bottleneck. These traffic jams are usually related to instabilities in traffic flow. The applications of intelligent traffic systems are a potential solution to reduce the amplitude or to eliminate the formation of such traffic instabilities. A lot of research has been conducted to theoretically study the effect of intelligent vehicles, for example adaptive cruise control vehicles, using either computer simulation or analytical method. However, most current analytical research has only applied to single class traffic flow. To this end, the main topic of this paper is to perform a linear stability analysis to find the stability threshold of heterogeneous traffic flow using microscopic models, particularly the effect of intelligent vehicles on heterogeneous (or multi-class) traffic flow instabilities. The analytical results will show how intelligent vehicle percentages affect the stability of multi-class traffic flow.     

基于交通流的多模糊时间窗车辆路径优化

研究了基于交通流的多模糊时间窗车辆路径问题,考虑了实际中不断变化的交通流以及客户具有多个模糊时间窗的情况,以最小化配送总成本和最大化客户满意度为目标,构建基于交通流的多模糊时间窗车辆路径模型。根据伊藤算法的基本原理,设计了求解该模型的改进伊藤算法,结合仿真算例进行了模拟计算,并与蚁群算法的计算结果进行了对比分析,结果表明,利用改进伊藤算法求解基于交通流的多模糊时间窗车辆路径问题,迭代次数小,效率更高,能够在较短的时间内收敛到全局最优解,可以有效的求解多模糊时间窗车辆路径问题。     

基于新老司机道路选择行为的交通流均衡研究

针对新上路司机数量的爆发式增长带来的交通流均衡变化问题,本文在对司机进行分类和道路选择行为分析的基础上,应用决策树方法构建了基于新老司机道路选择行为的交通流均衡模型,并用实际案例研究了主要参数的敏感性。研究发现:路况通过联合系统车流量的分配情况、车速预期和司机学习过程等因素共同对司机比例产生影响;当某一条道路达到均衡时,车流量对司机比例的敏感程度受到路况差异的影响;司机在驾驶经验、对道路的熟悉程度以及学习能力等方面存在差异,但这种差异仅存在于对交通信息的感知方面。该研究有助于加深对城市交通流变化规律的认识和理解,对于发展出有效的交通管制措施有积极的理论价值和现实意义。     

主路多车道无信号交叉口混合交通流的通行能力

Highway capacity is defined as maximum volume of traffic flow through the particular highway section under given traffic conditions,road conditions and so on.Highway construction and management is judged by capacity standard.The reasonable scale and time of highway construction,rational network structure and optimal management mode of highway network can be determined by analyzing the fitness between capacity and traffic volume.All over the world,highway capacity is studied to different extent in different country. Based on the gap acceptance theory,the mixed traffic flow composed of two representative vehicle types heavy and light vehicles is analyzed with probability theory.Capacity model of the minor mixed traffic flows crossing m major lanes,on which the traffic flows fix in with M3 distributed headway,on the unsignalized intersection is set up,and it is an extension of minor lane capacity theory for one vehicle-type and one major-lane traffic flow.     

Payne-Whitham型宏观交通流模型波动特性

宏观交通流模型将交通流比拟成流体流,通过整体变量如交通流量、平均车速以及交通密度来研究其整体性质,得到了越来越多的肯定.文章采用波前展开的方法,研究Payne-Whitham型宏观交通流模型描述扰动沿交通流波动的特性,同时给出了相应的稳定性条件.最后利用Padé逼近法进行数值仿真,得到的结果与理论分析相一致.     

短时交通流混沌预测模型的比较研究

短时交通流预测是实现交通流诱导的关键技术之一.针对目前短时交通混沌预测模型预测结果差异较大的问题,归纳了4种基于混沌理论的短时交通流预测模型:RBF神经网络模型、最大Lyapunov指数模型、局域线性模型和Volterra滤波器自适应预测模型,并对这4种预测模型进行了比较研究.应用4种预测模型对几个典型的非线性系统进行预测,验证了算法的准确性.然后用这4种预测模型对微观实测交通流的时间序列进行实证分析.仿真结果表明,4种预测模型对典型混沌时间序列具有很好的预测效果;而对实测交通流预测,其预测精度和稳定性较差,但可以满足实时交通流预测的需要.     

A dynamical systems approach based on averaging to model the macroscopic flow of freeway traffic

The flow of traffic exhibits distinct characteristics under different conditions, reflecting the congestion during peak hours and relatively free motion during off-peak hours. This requires one to use different mathematical equations to describe the diverse traffic characteristics. Thus, the flow of traffic is best described by a hybrid system, namely different governing equations for the different regimes of response, and it is such a hybrid approach that is investigated in this paper. Existing models for the flow of traffic treat traffic as a continuum or employ techniques similar to those used in the kinetic theory of gases, neither of these approaches gainfully exploit the hybrid nature of the problem. Spurious two-way propagation of disturbances that are physically unacceptable are predicted by continuum models for the flow of traffic. The number of vehicles in a typical section of the highway does not justify its being modeled as a continuum. It is also important to recognize that the basic premises of kinetic theory are not appropriate for the flow of traffic (see [S. Darbha, K.R. Rajagopal, Limit of a collection of dynamical systems: an application to modeling the flow of traffic, Mathematical Models and Methods in Applied Sciences 12 (10) (2002) 1381–1399] for a rationale for the same). A model for the flow of traffic that does not treat traffic as a continuum or use notions from kinetic theory is developed here and corroborated with real-time data collected on US 183 in Austin, Texas. Predictions based on the hybrid system model seem to agree reasonably well with the data collected on US 183.