最小一乘估计的最优化方法与灵敏度分析

最小一乘估计是人们最常用的回归方法之一,因为其回归结果受奇异点的影响较小,从而受到人们越来越多的关注,鉴于此方法所构造模型的非光滑性,进而增加了其计算的难度.针对不同观测结果及需求,将最小一乘模型转化成不同的线性规划模型,利用相应的求解软件进行求解.并针对不同情况对结果进行了灵敏度分析,从而找出了影响结果的因素.     

A modest proposal: an approach to making the internal R system extensible

The R computing environment has become an important part of the statistical community and fostered the development of over a thousand add-on packages, many representing state-of-the-art research in statistical methodology. Although it is relatively easy to develop functionality on top of the system, it is very difficult for developers to directly extend the core system itself—the language, the interpreter and the internal data structures. Yet the ability to easily introduce new core, first-class data structures into the system that are customized and efficient is becoming essential in this era of large, complex data sets and innovative algorithms and data structures. While the community that might use such a facility to introduce new data types may be small, it is potentially very talented and important, and may lead to significant innovations that allow us to continue to leverage R for the next 5 years or more in rich new ways. I describe some of the difficulties that people encounter in extending the system and suggest that an object-oriented architecture for the internal implementation of R (or any system) would make such low-level internals extensible by package developers and not just the core development team. This would promote potentially rich experimentation that would allow us and others to approach new styles of computation in R, while simultaneously maintaining the existing important community which provides so much value-added to the R environment. Specifically, transforming the R implementation from a representation-specific architecture to a C++ abstract/virtual interface-based architecture may be the least disruptive approach to the continued evolution of R, and would bring many advantages and some technical challenges. Such an approach involves many technical details and potential degradations in performance. Due to the length of the this paper, I do not explore these issues in great detail but introduce the basic concepts. I do, however, refer to some technical aspects that are best understood with some knowledge of the implementation of R at the level of using the .Call () interface in R.     

Type II sensitivity analysis of cost coefficients in the degenerate transportation problem

This paper focuses on sensitivity analysis of the degenerate transportation problem (DTP) when perturbation occurs on one cost coefficient. The conventional Type I sensitivity analysis of the transportation problem (TP) determines the perturbation ranges for the invariant optimal basis. Due to different degenerate optimal basic solutions yielding different Type I ranges, the Type I range is misleading for the DTP. Type II sensitivity analysis, which determines the perturbation ranges for the invariant shipping pattern, is more practical for the DTP. However, it is too tedious to obtain Type II ranges by enumerating all optimal basic solutions and all primal optimal basic solutions while getting the union of each corresponding Type I ranges. Here, we propose two labeling algorithms to determine the Type II ranges of the cost coefficient. Besides, three lemmas are provided for obtaining the upper bound or lower bound of the Type II ranges of the cost coefficient directly under specific conditions of the DTP. A numerical example is given to demonstrate the procedure of the proposed labeling algorithms and computational results have been provided.     

On the maximum number of feasible ranking sequences in multi-criteria decision making problems

In many decision problems the focus is on ranking a set of m alternatives in terms of a number, say n, of decision criteria. Given are the performance values of the alternatives for each one of the criteria and the weights of importance of the criteria. This paper demonstrates that if one assumes that the criteria weights are changeable, then the number of all possible rankings may be significantly less than the upper limit of m!. As a matter of fact, this paper demonstrates that the number of possible rankings is a function of the number of alternatives and the number of criteria. These findings are important from a sensitivity analysis point of view or when a group decision making environment is considered.     

Stability analysis of tree structured decision functions

In multicriteria decision problems many values must be assigned, such as the importance of the different criteria and the values of the alternatives with respect to subjective criteria. Since these assignments are approximate, it is very important to analyze the sensitivity of results when small modifications of the assignments are made. When solving a multicriteria decision problem, it is desirable to choose a decision function that leads to a solution as stable as possible. We propose here a method based on genetic programming that produces better decision functions than the commonly used ones. The theoretical expectations are validated by case studies.     

Multicriterion decision making in performance evaluation of an irrigation system

The selection of the best alternative in irrigation development strategies is examined in the multiobjective context. Sri Ram Sagar Project, a major irrigation project in India is taken for the case study. The study deals with the performance evaluation of five canal distributories by considering eight different criteria. Two Multicriterion Decision Making (MCDM) methods, namely, Multi Attribute Utility Theory (MAUT) and Stochastic extension of PROMETHEE-2 (STOPROM-2) are employed to select the best one among the five. Taguchi experimental design technique is employed to minimise the computational burden arising in the sensitivity analysis studies. The proposed methodology can serve as a model to choose the best one for formulating guide lines for improving the efficiency and performance of similar other distributories.     

Application of fuzzy soft set in decision making problems based on grey theory

There are many uncertain problems in practical production and life which need decisions made with soft sets and fuzzy soft sets. However, the basis of evaluation of the decision method is single and simple, the same decision problem can obtain different results from using a different evaluation basis. In this paper, in order to obtain the right result, we discuss fuzzy soft set decision problems. A new algorithm based on grey relational analysis is presented. The evaluation bases of the new algorithm are multiple. There is more information in a decision result based on multiple evaluation bases, which is more easily accepted and logical to one’s thinking. For the two cases examined, the results show that the new algorithm is efficient for solving decision problems.     

目标函数系数与约束右端项同时变化的灵敏度分析

灵敏度分析应用很广,但是人们对灵敏度的讨论往往局限于单个参数发生变化对求解结果的影响.本文主要讨论目标函数系数C和约束右端项b两个参数同时改变对最优基、最优解及目标值的影响以及最优解发生变化时,如何求出新的最优解.     

Approaches to collective decision making with fuzzy preference relations

Recent experimental studies show that the predictive accuracy of many of the solution concepts derived from the collective decision making theory leaves much to be desired. In a previous paper the author attempted to explain some of the inaccuracies in terms of the fuzzy indifference regions of the individuals participating in the voting game. This paper gives straightforward generalizations of the solutions concepts in terms of the fuzzy social or individual preference relations. It turns out that some of these new solution concepts cotain their nonfuzzy counterparts as subsets. Others, in turn, are subsets of their nonfuzzy counterparts. We also discuss a method of aggregating individual nonfuzzy preferences so as to get a fuzzy social preference relation and, furthermore, a nonfuzzy social choice set.     

An experimental study of the effect of uncertainty representation on decision making

This paper presents the results of an experiment investigating the effects of using different formats for representing uncertain attribute evaluations on decision making. Study participants make a series of hypothetical choices using six uncertainty formats - probability distributions, expected values, standard deviations, three-point (minimum-median-maximum) approximations, quantiles, and scenarios - and effects on decision making are tracked in terms of the quality of the final choice, the specific characteristics of the selected alternatives, and the difficulty experienced in making a decision. The results provide insights into how subjects make single- and multi-criteria choices in the presence of uncertainty (and some format for representing uncertainty) but in the absence of any real facilitation. The use of probability distributions appeared to overload subjects with information, leading to poorer and more difficult choices than if some intermediate level of summary was used - in particular three-point approximations or quantiles.     

运用因子分析法建立教学质量评估指标体系

在大量抽样调查的基础上，本文运用因子分析（Ｆａｃｔｏｒ Ａｎａｌｙｓｉｓ）的方法，在Ｍ—３４０计算机上利用ＡＮＡＬＹＳＴ统计分析软件包中因子分析软件程序，求得因子载荷矩阵．依据因子载荷矩阵，并结合教学质量评估的特点，建立起适用于学生为参评者的教学质量评估指标体系．     

Characterization of perturbed mathematical programs and interval analysis

Several authors have used interval arithmetic to deal with parametric or sensitivity analysis in mathematical programming problems. Several reported computational experiments have shown how interval arithmetic can provide such results. However, there has not been a characterization of the resulting solution interval in terms of the usual sensitivity analysis results. This paper presents a characterization of perturbed convex programs and the resulting solution intervals.Interval arithmetic was developed as a mechanism for dealing with the inherent error associated with numerical computations using a computational device. Here it is used to describe error in the parameters. We show that, for convex programs, the resulting solution intervals can be characterized in terms of the usual sensitivity analysis results. It has been often reported in the literature that even well behaved convex problems can exhibit pathological behavior in the presence of data perturbations. This paper uses interval arithmetic to deal with such problems, and to characterize the behavior of the perturbed problem in the resulting interval. These results form the foundation for future computational studies using interval arithmetic to do nonlinear parametric analysis.     

PARADIGM SHIFTS IN FISHERIES STOCK ASSESSMENT: FROM INTEGRATED ANALYSIS TO BAYESIAN ANALYSIS AND BACK AGAIN

ABSTRACT. I describe integrated analysis and Bayesian analysis, which have been two of the most influential paradigms in fisheries stock assessment during the last two decades of the twentieth century. These two paradigms have generally been considered complementary, rather than competing. However, recent advances in integrated analysis, including the special case of meta‐analysis, have made Bayesian analysis somewhat redundant. I describe how data used to create priors for use in Bayesian analysis can be integrated directly into the analyses. This provides a much more convenient way of accurately including the information and associated uncertainty into the analyses. I discuss how there is still a need to describe the uncertainty and suggest that research should focus on the most appropriate methods for doing this.     

Image Denoising by a Local Clustering Framework

Images often contain noise due to imperfections in various image acquisition techniques. Noise should be removed from images so that the details of image objects (e.g., blood vessels, inner foldings, or tumors in the human brain) can be clearly seen, and the subsequent image analyses are reliable. With broad usage of images in many disciplines—for example, medical science—image denoising has become an important research area. In the literature, there are many different types of image denoising techniques, most of which aim to preserve image features, such as edges and edge structures, by estimating them explicitly or implicitly. Techniques based on explicit edge detection usually require certain assumptions on the smoothness of the image intensity surface and the edge curves which are often invalid especially when the image resolution is low. Methods that are based on implicit edge detection often use multiresolution smoothing, weighted local smoothing, and so forth. For such methods, the task of determining the correct image resolution or choosing a reasonable weight function is challenging. If the edge structure of an image is complicated or the image has many details, then these methods would blur such details. This article presents a novel image denoising framework based on local clustering of image intensities and adaptive smoothing. The new denoising method can preserve complicated edge structures well even if the image resolution is low. Theoretical properties and numerical studies show that it works well in various applications.     

MOIRA: A decision support system for decision making on aquatic ecosystems contaminated by radioactive fallout

Interventions to restore radionuclide contaminated aquatic ecosystems may reduce individual and collective radiation doses, but may also result in detrimental ecological, social and economic effects. Decision makers must carefully evaluate possible impacts before choosing a countermeasure, hence decision analysis methods constitute an important aid to rank intervention strategies after the contamination of an aquatic ecosystem. We describe MOIRA, a decision support system for the identification of optimal remedial strategies to restore water systems after accidental introduction of radioactive substances. MOIRA includes an evaluation module based on a multi-attribute value model to rank alternatives and a module to perform multiparametric sensitivity analyses, both with respect to weights and values, to allow us to gain insights into the problem. The problem is under certainty since the validation of models used to quantify countermeasure impacts suggests little uncertainty in policy effects.The system is implemented in a PC based decision support system which allows the inclusion of all relevant information.     

Spatial competition facility location models: Definition,formulation and solution approach

Models are presented for locating a firm's production facilities and determining production levels at these facilities so as to maximize the firm's profit. These models take into account the changes in price at each of the spatially separated markets that would result from the increase in supply provided by the new facilities and also from the response of competing firms. Two different models of spatial competition are presented to represent the competitive market situation in which the firm's production facilities are being located. These models are formulated as variational inequalities; recent sensitivity analysis results for variational inequalities are used to develop derivatives of the prices at each of the spatially separated markets with respect to the production levels at each of the new facilities. These derivatives are used to develop a linear approximation of the implicit function relating prices to productions. A heuristic solution procedure making use of this approximation is proposed.     

Optimal and canonical solutions of the change making problem

Given a set of different coin-types, the change-making problem consists in assembling a changes c so as to minimize the number of coins utilized; this problem can arise in practice in some classes of uni-dimensional cargo-loading and cutting-stock problems. The paper presents a depth-first branch and bound algorithm, which makes use of a new dominance criterion; the superiority of this algorithm over Chang-Gill's and Wright's is shown through extensive computational comparisons. Moreover the performance and the applicability of a heuristic algorithm are analyzed.     

Multicriteria decision making on maintenance: Spares and contracts planning

The competitiveness of an industrial system is directly related to decision making in areas of product support logistics, such as the maintenance area. Multicriteria decision making takes into account various aspects associated with competitiveness of the system. This paper presents multicriteria decision models for two maintenance problems: repair contract selection and spares provisioning. In the repair contract problem the model incorporates consequences modelled through a multiattribute utility function. These consequences consist of contract cost and system performance, represented by the system interruption time. Two criteria (risk and cost) are combined through a multiattribute utility function in the spares provisioning decision model. This paper presents the formulation and derivations for both models and the numerical application illustrates the use of models including sensitivity analysis.     

具有相型服务分布的排队系统的性能灵敏度分析

具有非线数服务分布的排队网络已被广泛应用于许多领域,如通讯网络和管理系统。本文借助于无穷小说矩阵摄动方法,研究了M/PH/1排队系统的稳态性能灵敏度分析问题,给出了性能灵敏度公式,并表明了稳态性能灵敏度很容易通过系统势能进行计算。同时,给出一种计算势能及性能导数的算法。这个算法可直接用于系统的控制与优化,因为它基于分析系统的一条单一样本轨道。最后提供一个数值例子来表明这个算法的应用。