Resampling methods for ranked set samples

When measuring units are expensive or time consuming, while ranking them can be done easily, it is known that ranked set sampling (RSS) is preferred to simple random sampling (SRS). Available results for RSS are developed under specific parametric assumptions or are asymptotic in nature, with few results available for finite size samples when the underlying distribution of the observed data is unknown. We investigate the use of resampling techniques to draw inferences on population characteristics. To obtain standard error and confidence interval estimates we discuss and compare three methods of resampling a given ranked set sample. Chen et al. (2004. Ranked Set Sampling: Theory and Applications. Springer, New York) suggest a natural method to obtain bootstrap samples from each row of a RSS. We prove that this method is consistent for a location estimator. We propose two other methods that are designed to obtain more stratified resamples from the given sample. Algorithms are provided for these methods. We recommend a method that obtains a bootstrap RSS from the observations. We prove several properties of this method, including consistency for a location parameter. We define two types of L-estimators for RSS and obtain expressions for their exact moments. We discuss an application to obtain confidence intervals for the Winsorized mean of a RSS.     

An empirical assessment of ranking accuracy in ranked set sampling

Ranked set sampling (RSS) involves ranking of potential sampling units on the variable of interest using judgment or an auxiliary variable to aid in sample selection. Its effectiveness depends on the success in this ranking. We provide an empirical assessment of RSS ranking accuracy in estimation of a population proportion.     

A bootstrap test for symmetry based on ranked set samples

To test the hypothesis of symmetry about an unknown median we propose the maximum of a partial sum process based on ranked set samples. We discuss the properties of the test statistic and investigate a modified bootstrap ranked set sample bootstrap procedure to obtain its sampling distribution. The power of the new test statistic is compared with two existing tests in a simulation study.     

Algorithms and applications for answering ranked queries using ranked views

Ranked queries return the top objects of a database according to a preference function. We present and evaluate (experimentally and theoretically) a core algorithm that answers ranked queries in an efficient pipelined manner using materialized ranked views. We use and extend the core algorithm in the described PREFER and MERGE systems. PREFER precomputes a set of materialized views that provide guaranteed query performance. We present an algorithm that selects a near optimal set of views under space constraints. We also describe multiple optimizations and implementation aspects of the downloadable version of PREFER. Then we discuss MERGE, which operates at a metabroker and answers ranked queries by retrieving a minimal number of objects from sources that offer ranked queries. A speculative version of the pipelining algorithm is described.Received: 10 June 2002, Accepted: 11 June 2002, Published online: 30 September 2003Edited by: A. MendelzonWork supported by NSF Grant No. 9734548.     

利用条件概率和Gibbs抽样技术为分布估计算法构造通用概率模型

本文针对传统分布估计算法在建立概率模型时面临的各种困难,提出一种基于条件概率和Gibbs抽样的概率模型,能有效改进分布估计算法的通用性.使用该模型的分布估计算法利用进化过程中有前途的优秀个体构造出多个监督学习样本集,并对每个样本集估计出对应分量的条件概率,再使用这一组条件概率进行Gibbs抽样产生新的个体替代种群中的劣等个体.通过仿真实验表明,改进后的算法能够求解出可加性降解函数的全局最优解,表现出较强的全局优化能力.     

基于概率分布估计的混合采样算法

在类别不均衡的数据中, 类间和类内不均衡性问题都是导致分类性能下降的重要因素. 为了提高不均衡数据集下分类算法的性能, 提出一种基于概率分布估计的混合采样算法. 该算法依据数据概率分别对每个子类进行采样以保证类内的均衡性; 并扩大少数类的潜在决策域和减少多数类的冗余信息, 从而同时从全局和局部两个角度改善数据的平衡性. 实验结果表明, 该算法提高了传统分类算法在不均衡数据下的分类性能.

     

Evaluating the precision of eight spatial sampling schemes in estimating regional means of simulated yield for two crops

We compared the precision of simple random sampling (SimRS) and seven types of stratified random sampling (StrRS) schemes in estimating regional mean of water-limited yields for two crops (winter wheat and silage maize) that were simulated by fourteen crop models. We found that the precision gains of StrRS varied considerably across stratification methods and crop models. Precision gains for compact geographical stratification were positive, stable and consistent across crop models. Stratification with soil water holding capacity had very high precision gains for twelve models, but resulted in negative gains for two models. Increasing the sample size monotonously decreased the sampling errors for all the sampling schemes. We conclude that compact geographical stratification can modestly but consistently improve the precision in estimating regional mean yields. Using the most influential environmental variable for stratification can notably improve the sampling precision, especially when the sensitivity behavior of a crop model is known.     

An adaptive surrogate modeling-based sampling strategy for parameter optimization and distribution estimation (ASMO-PODE)

Parameter distribution estimation has long been a hot issue for the uncertainty quantification of environmental models. Traditional approaches such as MCMC (Markov Chain Monte Carlo) are prohibitive to be applied to large complex dynamic models because of the high computational cost of computing resources. To reduce the number of model evaluations required, we proposed an adaptive surrogate modeling-based sampling strategy for parameter distribution estimation, named ASMO-PODE (Adaptive Surrogate Modeling-based Optimization – Parameter Optimization and Distribution Estimation). The ASMO-PODE can provide an estimation of the parameter distribution using as little as one percent of the model evaluations required by a regular MCMC approach. The effectiveness and efficiency of the ASMO-PODE approach have been evaluated with 2 test problems and one land surface model, the Common Land Model. The results demonstrated that the ASMO-PODE method is an economic way for parameter optimization and distribution estimation.     

Understanding and comparisons of different sampling approaches for the Fourier Amplitudes Sensitivity Test (FAST)

Fourier Amplitude Sensitivity Test (FAST) is one of the most popular uncertainty and sensitivity analysis techniques. It uses a periodic sampling approach and a Fourier transformation to decompose the variance of a model output into partial variances contributed by different model parameters. Until now, the FAST analysis is mainly confined to the estimation of partial variances contributed by the main effects of model parameters, but does not allow for those contributed by specific interactions among parameters. In this paper, we theoretically show that FAST analysis can be used to estimate partial variances contributed by both main effects and interaction effects of model parameters using different sampling approaches (i.e., traditional search-curve based sampling, simple random sampling and random balance design sampling). We also analytically calculate the potential errors and biases in the estimation of partial variances. Hypothesis tests are constructed to reduce the effect of sampling errors on the estimation of partial variances. Our results show that compared to simple random sampling and random balance design sampling, sensitivity indices (ratios of partial variances to variance of a specific model output) estimated by search-curve based sampling generally have higher precision but larger underestimations. Compared to simple random sampling, random balance design sampling generally provides higher estimation precision for partial variances contributed by the main effects of parameters. The theoretical derivation of partial variances contributed by higher-order interactions and the calculation of their corresponding estimation errors in different sampling schemes can help us better understand the FAST method and provide a fundamental basis for FAST applications and further improvements.     

基于粗糙集的数据流多标记分布特征选择

针对传统特征选择算法无法处理流特征数据、冗余性计算复杂、对实例描述不够准确的问题,提出了基于粗糙集的数据流多标记分布特征选择算法。首先,将在线流特征选择框架引入多标记学习中;其次,用粗糙集中的依赖度替代原有的条件概率,仅仅利用数据自身的信息计算,使得数据流特征选择算法更加高效快捷;最后,由于在现实世界中,每个标记对实例的描述程度并不相同,为更加准确地描述实例,将传统的逻辑标记用标记分布的形式进行刻画。在多组数据集上的实验表明,所提算法能保留与标记空间有着较高相关性的特征,使得分类精度相较于未进行特征选择的有一定程度的提高。     

可变直觉模糊多粒度粗糙集模型及其近似分布约简算法

为了在多粒度粗糙集模型中对目标概念达到更好的近似逼近效果,首先将直觉模糊粗糙集与多粒度粗糙集结合,提出直觉模糊多粒度粗糙集模型。由于该模型的目标近似存在过于宽松的缺陷,因此通过引入参数的方式对所提模型进行改进,提出一种可变直觉模糊多粒度粗糙集模型,并证明了该模型的有效性,同时基于该模型提出了相应的近似分布约简算法。在仿真实验结果中,所提出的下近似分布约简结果比已提出的模糊多粒度决策理论粗糙集约简和多粒度双量化决策理论粗糙集多了2~4个属性,所提出的上近似分布约简算法比这些算法少了1~5个属性,同时约简结果的近似精度拥有了更为合理且优越的表现。因此,理论和实验结果均验证了所提的可变直觉模糊多粒度粗糙集模型在近似逼近和数据降维方面均具有更高的优越性。     

路径追踪中出射光线方向的快速采样方法

目的 基于双向反射分布函数的重要性采样方法在渲染物体材质表面时有极佳的拟真度,但采样方式存在复杂和高硬件存储开销的问题。针对上述问题,提出了一种基于权重生成和向量线性插值的采样方法用于解决该问题。方法 在对出射光线方向进行计算时,通过给定的入射光方向、法线方向与物体表面材质光滑度参数,首先计算镜面反射光线方向,再结合余弦与指数函数二者的函数特性生成具有一定分布特征的权重值,并将镜面反射方向与随机生成的漫反射方向进行线性插值,其插值权重即为上述生成的权重值,最后规范化得到具有一定分布特征的新的出射方向。结果 本文基于该快速采样方法,给出了路径追踪渲染算法的一套完整实现,并利用本文算法,从常见各类物体表面中抽取9种进行渲染,将所得实验结果与通过原始双向反射分布函数采样算法所渲染得到的实际结果进行比较,发现利用快速采样算法后渲染速度可提升1.521.99倍,且由于近似所造成的相对误差可控制在8%以内,并将原本用于描述物体表面的34 MB数据量降为仅几个浮点数的数据量,可知上述采样方法既具有极低硬件存储开销的特点,其渲染的图片又能保有较高的拟真度。随着光滑度参数的连续变化,可使得被渲染的物体表面由理想漫反射到理想镜面反射之间均匀过渡,从而统一了漫反射、高光反射与镜面反射三者的采样形式。结论 本文使用简化的出射光方向采样算法替代传统BRDF重要性采样算法,并配套给出基于新采样算法实现的一套完整的路径追踪渲染方法,使得在不失真实度的情况下使得计算机在模拟漫反射、高光反射与镜面反射的形式得以简化与统一。本文方法亦可作为现有诸多采样方法的替代方案,其极低的存储开销优势可用于渲染含有大量不同材质的复杂场景;在渲染一般的粗糙表面、瓷器以及金属等常见各向同性材质时也有较佳的表现力。上述的完整实现方式可以在需要的时候对静态场景做不失真实度的快速渲染。     

多采样频率的配网接地故障检测与定位

现有文献的故障监测与定位小波算法都是在录波采样频率相同的前提下进行的,配电网小电流接地故障实时检测,与变电站接地故障检测的环境完全不同：配网故障监测装置,采用不同标准采样频率(3600Hz、4800Hz)上送实时故障录波数据到配网中心,更有采用4096Hz的采样频率上送故障录波数据,在配网中心需要把不同采样频率的录波数据进行分析计算,提取故障特征、检测故障,确定故障首尾端,实现故障检测与定位。本文给出了小波能量特征的定义、不同采样频率能量特征的折算、基于能量特征的配电网接地故障监测与定位算法。多种采样频率下配网接地故障检测与定位,通过小波变换提取故障能量特征、将不同采样频率故障录波信号,折算到最低采样频率下的能量特征,然后根据能量特征来判别故障类型、确定故障首尾端。多采样频率的小波能量特征折算算法,对于类似的小波变换的使用场合,也有借鉴意义。     

On the sampling distribution of resubstitution and leave-one-out error estimators for linear classifiers

Error estimation is a problem of high current interest in many areas of application. This paper concerns the classical problem of determining the performance of error estimators in small-sample settings under a Gaussianity parametric assumption. We provide here for the first time the exact sampling distribution of the resubstitution and leave-one-out error estimators for linear discriminant analysis (LDA) in the univariate case, which is valid for any sample size and combination of parameters (including unequal variances and sample sizes for each class). In the multivariate case, we provide a quasi-binomial approximation to the distribution of both the resubstitution and leave-one-out error estimators for LDA, under a common but otherwise arbitrary class covariance matrix, which is assumed to be known in the design of the LDA discriminant. We provide numerical examples, using both synthetic and real data, that indicate that these approximations are accurate, provided that LDA classification error is not too large.     

Approximating probability distribution of circuit performance function for parametric yield estimation using transferable belief model

This paper applies the transferable belief model （TBM） interpretation of the Dempster-Shafer theory of evidence to approximate distribution of circuit performance function for parametric yield estimation. Treating input parameters of performance function as credal variables defined on a continuous frame of real numbers, the suggested approach constructs a random set-type evidence for these parameters. The corresponding random set of the function output is obtained by extension principle of random set. Within the TBM framework, the random set of the function output in the credal state can be transformed to a pignistic state where it is represented by the pignistic cumulative distribution. As an approximation to the actual cumulative distribution, it can be used to estimate yield according to circuit response specifications. The advantage of the proposed method over Monte Carlo （MC） methods lies in its ability to implement just once simulation process to obtain an available approximate value of yield which has a deterministic estimation error. Given the same error, the new method needs less number of calculations than MC methods. A track circuit of high-speed railway and a numerical eight-dimensional quadratic function examples are included to demonstrate the efficiency of this technique.     

Reachable set estimation for switched nonlinear positive systems with impulse and time delay

This paper deals with the reachable set estimation for the continuous‐time switched nonlinear positive systems with impulse, disturbance, and mixed time‐varying delays under the average dwell time switching. Based on a method developed in positive systems, sufficient conditions are established such that all solutions of the system converge exponentially to a ball. Both the bound of the reachable set and the convergence rate are determined explicitly. Compared with the existing result, the average dwell time given in this paper is less conservative. Finally, numerical examples demonstrate the effectiveness of our results.     

随机迭代算法的概率分布模型及应用

针对带概率的迭代函数系统，伴随概率在吸引子图像控制中的影响作用，文章提出了几种不同的概率分布模型，应用该模型可以对吸引子图像实现局部细节和整体形状的控制，并以树木的模拟为实例，通过计算机数值实验展示了所给模型的控制效果。此方法用于计算机模拟自然景物，计算简单，易于操作，效果较好。     

一种耦合功能集割裂解耦方法

以设计矩阵表示的耦合功能集为研究对象,针对耦合功能集中功能耦合的程度,给出了一种度量的方法;使用混沌思想改进了粒子群算法,以参数可行解的减少量为目标函数,实现了耦合功能的顺序规划。最后通过某汽车停车档的设计实例验证了算法的有效性。     

A hybrid fuzzy-statistical clustering approach for estimating the time of changes in fixed and variable sampling control charts

Control charts are the most popular Statistical Process Control (SPC) tools used to monitor process changes. When a control chart produces an out-of-control signal, it means that the process has changed. However, control chart signals do not indicate the real time of the process changes, which is essential for identifying and removing assignable causes and ultimately improving the process. Identifying the real time of the process change is known as change-point estimation problem. Most of the traditional change-point methods are based on maximum likelihood estimators (MLE) which need strict statistical assumptions. In this paper, first, we introduce clustering as a potential tool for change-point estimation. Next, we discuss the challenges of employing clustering methods for change-point estimation. Afterwards, based on the concepts of fuzzy clustering and statistical methods, we develop a novel hybrid approach which is able to effectively estimate change-points in processes with either fixed or variable sample size. Using extensive simulation studies, we also show that the proposed approach performs considerably well in all considered conditions in comparison to powerful statistical methods and popular fuzzy clustering techniques. The proposed approach can be employed for processes with either normal or non-normal distributions. It is also applicable to both phase-I and phase-II. Finally, it can estimate the true values of both in- and out-of-control states’ parameters.     

Elliptic Gabriel graph for finding neighbors in a point set and its application to normal vector estimation

Point-based shape representation has received increased attention in recent years, mainly due to its simplicity. One of the most fundamental operations for point set processing is to find the neighbors of each point. Mesh structures and neighborhood graphs are commonly used for this purpose. However, though meshes are very popular in the field of computer graphics, neighbor relations encoded in a mesh are often distorted. Likewise, neighborhood graphs, such as the minimum spanning tree (MST), relative neighborhood graph (RNG), and Gabriel graph (GG), are also imperfect as they usually give too few neighbors for a given point. In this paper, we introduce a generalization of Gabriel graph, named elliptic Gabriel graph (EGG), which takes an elliptic influence region instead of the circular region in GG. In order to determine the appropriate aspect ratio of the elliptic influence region of EGG, this paper also presents the analysis between the aspect ratio of the elliptic influence region and the average valence of the resulting neighborhood. Analytic and empirical test results are included.