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Bayesian Approach for Comparing Parameter Estimation of Regression Model for Outlier Data 离群数据回归模型参数估计比较的贝叶斯方法
Autcha Araveeporn, K. Kumnungkit
This research compares and contrasts the simple regression model's parameter estimation methods, which consisted of a dependent variable and one independent variable. Parameter estimation uses the ordinary least square method, Bayesian method, Markov Chain Monte Carlo (MCMC) method, and local weight Markov Chain Monte Carlo (LWMCMC) method. The standard method is the ordinary least square method, which uses the concept of minimum sum square error to estimate parameters for fitting the linear regression model. However, for a set of the parameter relating to the Bayesian approach, the use of prior and posterior distributions may affect the approximation of the Bayesian, MCMC, LWMCMC methods. This paper considers the ordinal least square method and Bayesian approach by estimating the parameter for outlier data while some data points are far from other observations. The independent variable is simulated from the contaminated normal distribution, and the error is simulated from the normal distribution that made the outlier data on dependent and independent variables for the several sample sizes as 20, 50, 100, and 200. The criterion of the best efficiency is considered by the minimum of the average mean square errors. Through simulation data, the Bayesian method presents the minimum of average mean square errors at the sample sizes 20 and 50. However, when the sample size value increases, the MCMC and LWMCMC method are the best efficiency method at the sample sizes 100 and 200, respectively.
本研究比较和对比了由一个因变量和一个自变量组成的简单回归模型的参数估计方法。参数估计采用普通最小二乘法、贝叶斯方法、马尔可夫链蒙特卡罗(MCMC)方法和局部权值马尔可夫链蒙特卡罗(LWMCMC)方法。标准方法是普通最小二乘法,它使用最小和平方误差的概念来估计参数,以拟合线性回归模型。然而,对于一组与贝叶斯方法相关的参数,使用先验和后验分布可能会影响贝叶斯,MCMC, LWMCMC方法的近似。本文采用有序最小二乘法和贝叶斯方法对离群数据进行参数估计。自变量从受污染的正态分布模拟,误差从正态分布模拟,使因变量和自变量的离群数据在几个样本量为20、50、100和200。最佳效率的标准是平均均方误差最小。通过仿真数据,贝叶斯方法给出了样本容量为20和50时平均均方误差的最小值。当样本量增大时,MCMC法和LWMCMC法分别在样本量为100和200时效率最高。
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引用次数: 0
A Decentralized Collaborative Strategy for PTZ Camera Network Tracking System using Graph Learning: Assessing strategies for information sharing in a PTZ camera network for improving vehicle tracking, via agent-based simulations 使用图学习的PTZ摄像机网络跟踪系统的分散协作策略:通过基于代理的模拟,评估PTZ摄像机网络中用于改进车辆跟踪的信息共享策略
Shaik Masihullah, Subu Kandaswamy
In this paper, we propose a collaborative strategy for an autonomous PTZ (Pan Tilt Zoom) camera network, for improved target vehicle tracking, in real-world traffic. In addition, we explore ways to improve the target-tracking system to adapt itself to unexpected changes in traffic patterns. In the exploration phase, the camera nodes utilize the target identification information shared among themselves in the network to learn a graph. The vertices represent the camera nodes, while edges represent links to immediate neighbors, and edge weights represent the distance between the nodes in terms of the time taken by the target vehicles. In the exploitation phase, once a target vehicle is identified, the camera broadcasts the information to the neighbors. In turn, the neighbors consult the graph to position themselves better for capturing footage of the target vehicle. We carried out two agent-based simulation experiments to test the strategy. In the first experiment, we compare the proposed strategy, which uses the learned graph, to a baseline where the cameras operate independently for scanning traffic. In the second experiment, we compare the strategy to an improved adaptive version of itself, in which the system learns online continuously by observing live traffic. The results show that our cooperative camera network outperforms the baseline and the adaptive strategy outperforms the static one.
在本文中,我们提出了一个自主PTZ (Pan Tilt Zoom)摄像机网络的协作策略,以改善现实交通中的目标车辆跟踪。此外,我们还探索了改进目标跟踪系统的方法,以适应交通模式的意外变化。在探索阶段,相机节点利用网络中彼此共享的目标识别信息来学习图。顶点表示摄像机节点,边缘表示到近邻的链接,边缘权重表示节点之间的距离,以目标车辆所花费的时间为依据。在利用阶段,一旦识别出目标车辆,摄像机就会将信息广播给相邻车辆。然后,邻居们查看图表,以便更好地捕捉目标车辆的镜头。我们进行了两个基于智能体的仿真实验来测试该策略。在第一个实验中,我们将提出的策略(使用学习图)与相机独立运行扫描流量的基线进行比较。在第二个实验中,我们将该策略与自身的改进自适应版本进行比较,其中系统通过观察实时流量持续在线学习。结果表明,我们的协同摄像机网络优于基线,自适应策略优于静态策略。
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引用次数: 1
Convolving Hyper-Erlang with Hyper-Exponential Distributions Using Linear Algebra 用线性代数卷积超erlang与超指数分布
Clemens Neumüller, J. Robert, A. Heuberger
In this paper, the sum of a hyper-Erlang and a hyper-exponential distributed random variables is analyzed. Although tedious, the resulting random variable’s probability density function (PDF) can be obtained through convolution of its summands’ PDFs. Alternatively, the resulting distribution can be stated directly in terms of a phase-type distribution. However, computing its PDF can still be very costly and this representation gives little insight on the distribution. It can be shown that the sum of both random variable is again hyper-Erlang distributed of incremented order and can therefore be described without requiring the matrix exponential function. We derive a closed form linear algebra expression for the probability weights of the sum’s hyper-Erlang distribution, which significantly reduces the computational complexity of evaluating its distribution.
本文分析了超erlang和超指数分布随机变量的和。随机变量的概率密度函数(PDF)虽然繁琐,但可以通过对其和项的PDF进行卷积得到。或者,得到的分布可以直接用相型分布来表示。然而,计算它的PDF仍然是非常昂贵的,并且这种表示对分布没有什么深入的了解。可以证明,这两个随机变量的和又是增量阶的超厄朗分布,因此可以不需要矩阵指数函数来描述。我们对和的超erlang分布的概率权导出了一个封闭形式的线性代数表达式,大大降低了计算其分布的计算复杂度。
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引用次数: 1
Pricing Model of Insurance Product for Autistic Persons 孤独症患者保险产品定价模型研究
Zhiheng Jiang, Jiahao Fan, Qiyi Wang
This paper proposes a pricing model of insurance for persons with autism and further designs a possible insurance product that compensate the insured persons 18 years after purchasing the insurance. Using MATLAB programming, the variation of insurance premium with insurance parameters are plotted to analyze the effect of the insured years, the chance to diagnose a child as autism and the compensation pay-outs for non-autism on the breakeven insurance premium. The analytical results of the pricing model shows that there are a nonlinear relationship between the insurance premium and the insured years, a linear relationship between the insurance premium and the compensation pay-outs, a linear relationship between the insurance premium and the annuity insurance sent back to a non-autism insured, and a linear relationship between the insurance premium and the chance to diagnose a child as autistic. This work also establishes a model to calculate the profit generated from this insurance product.
本文提出了自闭症患者保险的定价模型,并进一步设计了一种可能的保险产品,在购买保险后对被保险人进行18年的赔偿。利用MATLAB编程,绘制保费随保险参数的变化曲线,分析投保年限、诊断为自闭症的几率和非自闭症的赔付额对保本保费的影响。定价模型的分析结果表明,保费与投保年限之间存在非线性关系,保费与赔偿金额之间存在线性关系,保费与返还给非自闭症被保险人的年金之间存在线性关系,保费与诊断为自闭症的机会之间存在线性关系。本工作还建立了一个模型来计算该保险产品产生的利润。
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引用次数: 0
Risk Factors Associated with Hospital Unwarned Appointment Absenteeism: A logistic binary regression approach 与医院无预警预约缺勤相关的危险因素:logistic二元回归方法
Miguel Maia, A. Borges, Mariana Cavalho
One of the main problems faced by health institutions is the unwarned absenteeism of patients in medical appointments. Patients’ no-shows, without prior notice, can result in loss of revenue for health centres and increasing waiting lines. Hence, there is a need to predict the non-attendance of patients to improve health institutions’ management performance. In this paper, a brief literature review was carried out to understand which factors can be related to patients’ absenteeism, and which forecasting methods are often applied to discover patterns in health datasets. As the logistic binary regression model has been proved to be effective on that matter, it was applied to a real hospital data set comprising information on 98.511 patients, with a corresponding 645.576 appointments, in a period between 2018 and 2020. Results indicate a significant effect on the chance of appointment attendance of patient age, patient gender, patient Marital Status, number of previous appointments, appointment month, precipitation levels, Lead time, and the number of previous no-show appointments.
保健机构面临的主要问题之一是病人在预约医疗时未事先通知就缺勤。患者在没有事先通知的情况下不来就诊,可能导致保健中心的收入损失,并增加排队等候的人数。因此,有必要预测患者的缺席,以提高卫生机构的管理绩效。本文通过简要的文献综述,了解哪些因素与患者缺勤有关,以及哪些预测方法通常用于发现健康数据集中的模式。由于逻辑二元回归模型已被证明在这方面是有效的,因此将其应用于一个真实的医院数据集,该数据集包含2018年至2020年期间98511名患者的信息,对应的645.576次预约。结果表明,患者年龄、患者性别、患者婚姻状况、既往预约次数、预约月份、降水水平、前置时间和既往未到预约次数对预约出诊率有显著影响。
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引用次数: 0
Performance Improvement of Logistic Regression for Binary Classification by Gauss-Newton Method 高斯-牛顿方法对Logistic回归二分类性能的改进
M. Jamhuri, I. Mukhlash, M. I. Irawan
This paper proposes a new approach to optimizing cost function for binary logistic regression by the Gauss-Newton method. This method was applied to the backpropagation phase as a part of the training process to update the weighted coefficients. To show the performance of the approach, we used two data sets to train the logistic regression model for binary classification problems. Our experiment demonstrated that the proposed methods could perform better than gradient descent for both examples, as we expected. Furthermore, the performance of our approach is more advanced than the classical method, either in speed or accuracy.
本文提出了一种利用高斯-牛顿法优化二元逻辑回归成本函数的新方法。将该方法应用于反向传播阶段,作为训练过程的一部分来更新加权系数。为了展示该方法的性能,我们使用两个数据集来训练二元分类问题的逻辑回归模型。我们的实验表明,对于这两个例子,我们所提出的方法可以比梯度下降更好,正如我们所期望的那样。此外,无论在速度还是精度上,我们的方法都比传统方法更先进。
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引用次数: 0
Stock price prediction based on PCA-LSTM model 基于PCA-LSTM模型的股票价格预测
Xinyuan Zheng, Naiping Xiong
In order to improve the prediction accuracy, this study proposes an new PCA-LSTM neural network stock price prediction model that combines principal component analysis(PCA) and long-term and short-term memory neural network (LSTM). We download time series indicators and technical indicators of PingAn insurance (X601318) form Tushare interface and Wind database. PCA method was used to reduce the technical indicators dimension, LSTM model was used to predict the next day stock closing price. The results show that PCA-LSTM model can greatly reduce data redundancy and obtain better prediction accuracy compared with the simple LSTM model. Additional Keywords and Phrases: stock price prediction, PCA, LSTM
为了提高预测精度,本研究提出了一种结合主成分分析(PCA)和长短期记忆神经网络(LSTM)的PCA-LSTM神经网络股票价格预测模型。我们从图共享接口和风德数据库中下载平安保险(X601318)的时间序列指标和技术指标。采用主成分分析法降维技术指标,采用LSTM模型预测翌日股票收盘价。结果表明,与简单的LSTM模型相比,PCA-LSTM模型可以大大减少数据冗余,获得更好的预测精度。附加关键词:股价预测,PCA, LSTM
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引用次数: 1
Research on the Equation of the Magnetic Field Caused by Magnets 磁体磁场方程的研究
Jia Su, Qingfei Shu
In this paper, the variational form is used to analyze the existence and uniqueness of the corresponding partial differential equations. In addition, the equation of the magnetic field induced by the magnet is also investigated. By constructing the corresponding Hilbert space and variational formulation, we can deduce that the equation admits a unique solution under some assumptions.
本文利用变分形式分析了相应的偏微分方程的存在唯一性。此外,还研究了磁体感应磁场的方程。通过构造相应的Hilbert空间和变分公式,我们可以推导出该方程在某些假设下存在唯一解。
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引用次数: 0
A Comparative Study of HiCanu and Hifiasm HiCanu和Hifiasm的比较研究
Yuqiu Wang
The recent development of Hifi sequencing has greatly improved people's understanding of genomics. Hifi reads provide a more accurate and complete picture than traditional long reads and Illumina short reads. However, both long reads and short reads assemblers are not good fits for Hifi reads in reality. Therefore, in late 2020, HiCanu and Hifiasm have been developed to assemble Hifi reads. Even though they are both phased assemblers, which highly complexed regions will be separated into two different alleles, they show different output formats, algorithms and performance. The topic of this paper will be focused on comparison between HiCanu and Hifiasm on contiguity, completeness, and runtime. In order to compare the two tools, it is necessary to examine HiCanu and Hifiasm results of different genome assemblies from several published papers. Despite some shortcomings of Hifiasm assembler which is associated with increased coverage, Hifiasm is the best assembler for Hifi reads so far because of its high contiguity, completeness and fast runtime.
近年来Hifi测序技术的发展,极大地提高了人们对基因组学的认识。Hifi读取比传统的长读取和Illumina短读取提供更准确和完整的图像。然而,在现实中,长读和短读汇编器都不适合高保真读。因此,在2020年底,HiCanu和Hifiasm已被开发用于组装Hifi读取。尽管它们都是将高度复杂的区域分成两个不同的等位基因的相控装配程序,但它们的输出格式、算法和性能都有所不同。本文的主题将集中在HiCanu和Hifiasm在连续性、完整性和运行时方面的比较。为了比较这两种工具,有必要从几篇已发表的论文中检验不同基因组组装的HiCanu和Hifiasm结果。尽管Hifiasm汇编器存在一些与增加覆盖相关的缺点,但由于Hifiasm的高连续性、完整性和快速运行,它是迄今为止Hifi读取的最佳汇编器。
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引用次数: 0
A new proposal of power series method to solve the Navier-Stokes equations: application contexts and perspectives 幂级数法求解Navier-Stokes方程的一种新方法:应用背景与前景
P. Lecca, Angela Re
In this work we investigate the possibility of expressing the solution of the Navier-Stokes equations as a power series. Although there have been many studies on this subject, it is still much debated. The existence of such a solution and its uniqueness are debated, especially in the general case of a non-stationary fluid in two or three dimensions. The greater the complexity of the fluid dynamical phenomenon under consideration, the more controversial and therefore uncertain are the deductions about the existence and uniqueness of the solution as a power series. Here, we ask some crucial questions on the matter and try to give an answer from the point of view of applied mathematics and numerical analysis. In particular, by way of example, we construct the Navier-Stokes equations for a compressible, multicomponent and non-stationary fluid from elementary principles of conservation of mass, momentum and energy, and we introduce a bump function model for the presence of different components and/or different phases in the fluid. The bump function is a function of space, time and physical characteristics of the components (and/or phases) such as density. We present a method to calculate it and discuss about its uniqueness. We show that under certain conditions on the bump function, and the forces acting on and in the fluid, the power series solution is unique. We finally discuss the advantages and the limitations of a solution in power series, concluding that, although plagued by limitations, it is a viable way forward even in highly complex case studies.
在这项工作中,我们研究了用幂级数表示Navier-Stokes方程解的可能性。虽然已经有很多关于这个问题的研究,但仍有很多争论。这种解的存在性及其唯一性一直受到争论,特别是在二维或三维非定常流体的一般情况下。所考虑的流体动力现象越复杂,关于解作为幂级数的存在性和唯一性的推论就越有争议,因而也就越不确定。在这里,我们提出了一些关键的问题,并试图从应用数学和数值分析的角度给出答案。特别地,通过举例,我们从质量、动量和能量守恒的基本原理出发,构造了可压缩、多组分和非稳态流体的Navier-Stokes方程,并引入了流体中存在不同组分和/或不同相的碰撞函数模型。凹凸函数是空间、时间和组件(和/或相)的物理特性(如密度)的函数。给出了一种计算它的方法,并讨论了它的唯一性。我们证明了在碰撞函数和作用于流体的力的一定条件下,幂级数解是唯一的。最后,我们讨论了幂级数解的优点和局限性,得出结论,尽管存在局限性,但即使在高度复杂的案例研究中,它也是一种可行的方法。
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引用次数: 0
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Proceedings of the 2022 5th International Conference on Mathematics and Statistics
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