列联表中辅助交互作用的可压缩性

本文对高维列联表中关于随机变量间的一种关联系数辅助交互作用的简单可压缩性与强可压缩性进行了讨论得到了一组对应的可压缩性的充分必要条件。     

Yule测度的可压缩性

Simpson悖论提醒人们在低维空间的统计推断可能会严重歪曲高维现实.针对该悖论,研究Yule测度的简单可压缩性、强可压缩性和连续可压缩性,给出这些可压缩性的充分必要条件.这些条件对于观测和试验研究设计、消除混杂偏倚、离散变量分类和水平划分等都有重要意义.     

离散事件动态系统的能达能观性与对干扰解耦的周期合并配置

能达与不能达子空间,能观与不能观子空间是 Wonham 教授创建的多变量控制几何方法的几个基本概念.对 DEDS 文献[2,3]提出了分别能达概念及其充要条件;文[2]还给出了与能达有关的标准结构;文[3]提出了上界能观及其充要条件;文[4]给出了用反馈合并周期的充分条件;文[5]得到了用输出反馈合并配置周期的充要条件.在以上文献     

隐变量交互作用分析建模及其在SAS上的实现

探讨隐变量交互作用分析的建模方法及其在SA S软件上的实现;首先阐述隐变量交互作用分析建模的原理,通过拟合一个隐变量交互作用分析示例,对加入交互作用项的统计分析结果与无交互作用项的统计分析结果进行对比;示例中交互作用项引起的变异在结果变量的总变异中占到79.20%.在应用结构方程模型分析隐变量产生的效应时,有时候不进行隐变量交互作用的分析可能会产生偏倚.     

非协调区域分解的Lagrangian乘子法

§1.引言 近年来随着并行计算机的迅速发展,求解椭圆型方程的区域分解法愈来愈引起人们的兴趣和重视.但是,目前能够见到的有限元区域分解法几乎都要求有限元空间在跨过子区域的边界时是协调的,必然限制有限元区域分解算法的优越性. [3]提出了一种非协凋区域分解法——非协调区域分解的杂交法.采用简化杂交法处理各子区域交界处的非协调性,这种方法在子区域的内部和边界采用两套不同的变量,允许内部变量在跨过各子区域的边界时不连续.但是这种方法有它的局限性,即要求边界变量在各子区域的顶点处必须保持连续性,这对推广到三维空间的情形带来很大的困难.本文提出一种非协调区域分解的Lagrangian乘子法,引进Lagrangian乘子来处理各子区域交界处的非协调性.这种方法也在子区域内部和边界采用两套不同的变量,它不仅允许内部变量在越过各子区域边界时的非协调性,并且还允许边界变量在各子区域的顶点处可以不连续,这就弥补了[3]的不足.同时,这种算法具有[3]的优点,即在不     

不连续系统的实用稳定性

实用稳定性的概念,首先在[2]中就连续系统的情形提出.在[3,4]中,继续对连续系统的情形作过讨论。而不连续系统实用稳定性的研究仅见于[5],其中只给出了三个判别准则(定理1～3)。本文系统地研究了不连续系统的实用稳定性,给出比文[5]广泛的各种实用稳定性的概念,得到了判别各种实用稳定性或实用不稳定性的一系列准则。     

一维分数阶渗透方程的数值模拟

<正>1引言渗流问题在水文、土壤、医学等许多研究领域被探讨.经典的整数阶渗透方程是在渗流连续的假设条件下建立的,但是这些假设在实际渗流中一般是不成立的,从而发展出能反映实际情况的分数阶渗透方程[1-3].最近几年在国际上掀起了一股求解分数阶微分方程研究热潮.Liu等人[4]通过变量变换得到分数阶对流色散方程的解;Meerschaert等人[5]提出空间分数阶微分方程的有     

关于Volterra型积分微分方程的稳定性

的零解的稳定性。这里A(t)是n×n阶函数矩阵,在[0,∞)上连续,C(t,s)是一个n×n阶函数矩阵,当0≤s≤t<∞时连续,且连续。文献[1]中利用对(1.1)构造泛函的方法,研究了以下问题:(Ⅰ)对(1.1)是一个纯量方程的情形,给出了在一定条件下,系统(1.1)的零解为稳定的充分必要条件;     

输出反馈极点配置问题的一个算法

在线性多变量控制理论中,存在一个代数特征值反问题——输出反馈极点配置问题。问题叙述如下: 问题PAO.给定A∈R~(n×n),B∈R_m~(n×m),C∈R_p~(p×n)和?={λ_1,λ_2,…,λ_n},?在复共轭下封闭.求K∈R~(m×p),使得A+BKC具有事先给定的特征值λ_1,λ_2,…,λ_n。 [2]和[5]等证明了     

部分潜入水中椭圆柱体振动分析*

本文在文献[1]的基础上,提出一种研究部分潜入水中椭圆柱体弯曲振动的解析法,并指出文献[2]的不足之处.作为特例,本文计算了考虑水体可压缩影响时的水中圆柱体的自振频率,给出了可压缩性影响范围.     

On collapsibilities of Yule’s measure

Simpson’s paradox reminds people that the statistical inference in a low-dimensional space probably distorts the reality in a high one seriously.To study the paradox with respect to Yule’s measure, this paper discusses simple collapsibility, strong collapsibility and consecutive collapsibility, and presents necessary and sufficient conditions of them.In fact, these conditions are of great importance for observational and experimental designs, eliminating confounding bias, categorizing discrete variables and so on.     

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??hen the distribution of random variable V_1,V_2 and V_3 composes an I\times J\times K contingency table, this paper research the collapsibility of entropy, and present necessary and sufficient conditions for simple collapsibility and strong collapsibility of mutual information by the research on collapsibility of entropy, which are considered under the condition of sub-independence.     

Collapsibility of Mutual Information

hen the distribution of random variable V_1,V_2 and V_3 composes an I\times J\times K contingency table, this paper research the collapsibility of entropy, and present necessary and sufficient conditions for simple collapsibility and strong collapsibility of mutual information by the research on collapsibility of entropy, which are considered under the condition of sub-independence.     

Some collapsibility results for n-dimensional contingency tables

For a multidimensional contingency table, we obtain several necessary and sufficient conditions for collapsibility and strict collapsibility, using the technique of Möbius inversion formula. As a consequence, the results of Whittemore (Journal of the Royal Statistical Society B, 40, 328–340, 1978) are stated in a form which is easy to understand and the proofs are much simpler and straightforward. Several new results on collapsibility and strict collapsibility with respect to more than one interaction parameter, are established, and their relationships to conditional independence are also pointed out. As applications of our results, several typical examples on collapsibility, strict collapsibility and conditional independence are discussed. It is also shown that Bishop et al. (Discrete Multivariate Analysis: Theory and Practice, MIT Press, Cambridge, 1975) conditions are necessary and sufficient for strict collapsibility with respect to a set of interaction factors.     

Preference Programming with incomplete ordinal information

This paper extends possibilities for analyzing incomplete ordinal information about the parameters of an additive value function. Such information is modeled through preference statements which associate sets of alternatives or attributes with corresponding sets of rankings. These preference statements can be particularly helpful in developing a joint preference representation for a group of decision-makers who may find difficulties in agreeing on numerical parameter values. Because these statements can lead to a non-convex set of feasible parameters, a mixed integer linear formulation is developed to establish a linear model for the computation of decision recommendations. This makes it possible to complete incomplete ordinal information with other forms of incomplete information.     

Non-additive robust ordinal regression: A multiple criteria decision model based on the Choquet integral

Within the multicriteria aggregation–disaggregation framework, ordinal regression aims at inducing the parameters of a decision model, for example those of a utility function, which have to represent some holistic preference comparisons of a Decision Maker (DM). Usually, among the many utility functions representing the DM’s preference information, only one utility function is selected. Since such a choice is arbitrary to some extent, recently robust ordinal regression has been proposed with the purpose of taking into account all the sets of parameters compatible with the DM’s preference information. Until now, robust ordinal regression has been implemented to additive utility functions under the assumption of criteria independence. In this paper we propose a non-additive robust ordinal regression on a set of alternatives A, whose utility is evaluated in terms of the Choquet integral which permits to represent the interaction among criteria, modelled by the fuzzy measures, parameterizing our approach.     

Assessing a set of additive utility functions for multicriteria decision-making,the UTA method

The purpose of the method presented in this paper is to assess additive utility functions which aggregate multiple criteria in a composite criterion, using the information given by a subjective ranking on a set of stimuli or actions (weak-order comparison judgments) and the multicriteria evaluations of these actions. It is an ordinal regression method using linear programming to estimate the parameters of the utility function.Stability and sensitivity analysis leads to the assessment of a set of utility functions by means of post-optimality analysis techniques in linear programming.Finally, a simple illustrative example is presented and some extensions of the method are proposed.     

Aggregation of ordinal information

Our interest is with the fusion of information which has an ordinal structure. Information fusion in this environment requires the availability of ordinal aggregation operations. Basic ordinal operations are first introduced. Next we investigate conjunctive and disjunction aggregations of ordinal information. The idea of a pseudo-log in the ordinal environment is presented. We discuss the introduction of a zero like point on an ordinal scale along with the related ideas of bipolarity (positive and negative values) and uni-norm aggregation operators. We introduce mean like aggregation operators as well weighted averages on a ordinal scale. The problem of selecting between ordinal models is considered.     

On rank reversal in decision analysis

Analytic hierarchy process (AHP) has been criticized for its possible rank reversal phenomenon caused by the addition or deletion of an alternative. This paper shows the fact that the rank reversal phenomenon occurs not only in the AHP but also in many other decision making approaches such as the Borda–Kendall (BK) method for aggregating ordinal preferences, the simple additive weighting (SAW) method, the technique for order preference by similarity to ideal solution (TOPSIS) method, and the cross-efficiency evaluation method in data envelopment analysis (DEA). Numerical examples are provided to illustrate the rank reversal phenomenon in these popular decision making approaches.