双线性因子分析

因子分析(factor analysis,FA)是一种流行的从多变量中提取公因子的统计技术,但它仅适用于向量值数据(每个数据点为一向量).当FA应用于矩阵值数据(每个数据点为一矩阵)时,一种常用的做法是首先将矩阵值观测向量化.然而,向量化使得因子分析面临两个问题:可解释性变差,容易陷入维数灾难.为了解决这两个问题,文章从矩阵值数据本身固有的矩阵结构出发,提出双线性因子分析(bilinear FA,BFA).新颖性在于BFA采用双线性变换,模型参数大大减少,有效克服了维数灾难问题,同时提取感兴趣的行变量和列变量公因子.文章开发了两种有效算法用于BFA模型参数的极大似然估计,讨论了估计的理论性质并明确地求出Fisher信息矩阵的解析表达式来计算参数估计的准确度,研究了BFA的模型选择问题.与传统因子得分为一向量不同,BFA的因子得分为一矩阵,文章为矩阵因子得分提供了计算方法以及可视化方法.最后,构建实证研究来理解提出的BFA模型并与相关方法进行比较.结果表明了BFA在矩阵值数据分析上的优越性和实用性.     

基于双变量Probit模型的间隙零门功能可靠性分析

爆炸间隙零门功能的实现,不仅与间隙的长度有关,还受控制通道截面积的影响.如何量化分析间隙零门功能可靠性与间隙长度及截面积的关系是工程技术领域关心的重要问题.综合考虑间隙长度、截面积及其交互影响,基于三元响应,提出了间隙零门成功响应的双变量Probit模型.利用得分统计量,分析了检验双变量Probit模型中两随机误差变量相关性的方法.同时还基于极大似然估计并结合双变量Probit模型,给出了模型参数的估计方法.最后基于一组模拟试验数据,利用双变量Probit模型,给出了该组数据下模型参数的估计结果以及间隙零门功能可靠性窗口的区域分布.     

我国国债规模对宏观经济影响实证分析

随着以希腊债务危机为导火索的欧洲债务危机的愈演愈烈,国债对宏观经济的影响再一次成为了经济学讨论的热点.首先从直观图形着手,运用H-P滤度法去除趋势后,计算各变量的偏离趋势百分比,对比国债规模代替变量与宏观经济效应代替变量之间的偏离趋势图,从图形得到的定量关系为后面的实证分析做好准备.然后进一步进行协整分析,并在向量自回归(VAR)框架下通过脉冲响应函数考察变量之间的相互影响路径,最后通过建立误差修正模型(ECM)分析各个变量之间的长期均衡关系和短期波动特征,以量化各变量之间影响程度的大小.全面系统地研究了国债对宏观经济增长的影响程度并做出实证分析,对于深刻认识国债的本质,规避国债的风险,科学合理地制定国债政策有着重要的理论价值和实际意义.     

利用贝叶斯网络分析基因表达数据

利用基因表达数据提出一种新的网络模型—贝叶斯网络,发现基因的互作.一个贝叶斯网络是多变量联合概率分布的有向图模型,表示变量间的条件独立属性.首先我们阐明贝叶斯网络如何表示基因间的互作,然后介绍从基因芯片数据学习贝叶斯网络的方法.     

模型集成误差与优化研究

将模型作为函数,模型的输入输出参数为变量,给出变量真值的定义。在此基础上,给出单一模型误差e,利用误差e求出模型输出变量真值的期望μ,用μ作为修正值以提高计算结果的精确度。通过给出模型集成误差λ的定义,详细推导了λ的计算方法,利用λ计算模型集成输出变量真值y的期望μy、方差σy2、σy2/vy2,μy作为最终计算结果的修正值,而σy2/vy2可作为模型集成选择的依据,对同一输出变量而言,σy2/vy2小的模型集成是较优的．     

高维数据下的贝叶斯网络结构学习

贝叶斯网络模型作为一种传统有效的大数据图模型,因其具有因果和概率性语义等特点受到学者们的广泛研究。为了解决基于高维数据构建贝叶斯网络的难题,本文提出了一种适用于高维数据的贝叶斯网络结构学习算法—LTB算法,该算法由Lasso、Tabu Search算法和BIC结合。首先,运用Lasso降低协变量的维数,筛选出与目标变量关系密切的协变量将作为贝叶斯网络的顶点。然后,选择Tabu Search作为元启发式算法,选择BIC作为计算得分的方法,两者结合构建全局最优的贝叶斯网络结构。实证分析表明,LTB算法应用于上证综指影响因素的研究,既可以获得上证综指与其影响因素间的因果关系,也可以利用条件概率得到上证综指影响因素间的组合方式。     

应用多维项目反应理论模型探索分数减法测验的维度识别

多维项目反应理论(MIRT)模型是国际教育统计与心理测量学研究的热点模型.在简要介绍一种常见的MIRT模型和数理统计学热门的变量筛选方法的基础上,针对教育统计研究者常用的分数减法测验数据进行测验题目的维度识别.通过分别使用传统的因子分析法、LASSO方法和弹性网方法分析测验数据,获得了测验题目的维度识别结果,并对它们的识别准确率进行比较.研究表明使用变量筛选方法尤其是LASSO方法能够较好地识别该测验的题目维度间隶属关系,为多维测验的维度识别提供可靠的信息.     

中医方药量化研究中方剂“归经强度”层次分析法模型和应用

初步探讨中医方药归经量化研究中方剂的"归经强度"模型和应用.根据中药归经理论,运用(量化)层次分析法进行研究,以四君子汤为例,给出中医方药归经量化中方剂"归经权重"和"归经强度"的计算模型.方剂归经强度模型能较准确的计算方剂的归经强度,不但创新了量化层次分析法而且实现了中医方剂"归经强度"差异性量化分析和合理性应用.     

混沌理论和灰色系统在农机总动力预测中的应用

农机总动力的预测可以为农业装备需求规划提供数据参考,以黑龙江省农机总动力数据作为研究对象,应用混沌理论中G-P算法计算农机总动力的关联维数,将求出的关联维数与灰色系统理论中的灰色关联分析法相结合研究其影响因素,建立了农机总动力灰色多变量预测模型GM(1,m).计算结果:应用Matlab软件编程计算得到了农机总动力7个具体的主导影响因素,并建立了农机总动力的灰色多变量GM(1,7)预测模型,模型的平均相对误差为2.14%,由结果对比可知该预测模型的预测结果高于GM(1,1),方法具有一定的预测精度与科学性.     

基于文本信息的上市中小企业财务困境预测研究

本文通过网络爬虫获取上市中小企业相关的文本信息,包括以年报为代表的信息披露报告和互联网新闻媒体报道的文本内容,采用词袋方法基于不同特征词词表对这些文本内容进行了量化分析,并以财务变量模型为基础对文本信息量化指标在财务困境预测中的作用进行了实证检验,结果表明由信息披露报告构建的管理层语调变量以及由新闻媒体报道构建的报道倾向变量、负面报道比例变量确实可以提高财务困境模型的拟合度和预测能力,而且在对不同类型文本信息的分析应有不同的侧重点。尽管本文针对的是上市中小企业,但并未考虑市场交易信息,因而可以推广到未上市交易的中小企业。     

Understanding How Students Develop Mathematical Models

in this article, we discuss findings from a research study designed to characterize students' development of significant mathematical models by examining the shifts in their thinking that occur during problem investigations. These problem investigations were designed to elicit the development of mathematical models that can be used to describe and explain the relations, patterns, and structure found in data from experienced situations. We were particularly interested in a close examination of the student interactions that appear to foster the development of such mathematical models. This classroom-based qualitative case study was conducted with precalculus students enrolled in a moderate-sized private research university. We observed several groups of 3 students each as they worked together on 5 different modeling tasks. In each task, the students were asked to create a quantitative system that could describe and explain the patterns and structures in an experienced situation and that could be used to make predictions about the situation. Our analysis of the data revealed 4 sources of mismatches that were significant in bringing about the occurrence of shifts in student thinking: conjecturing, questioning, impasses to progress, and the use of technology-based representations. The shifts in thinking in turn led to the development of mathematical models. These results suggest that students would benefit from learning environments that provide them with ample opportunity to express their ideas, ask questions, make reasoned guesses, and work with technology while engaging in problem situations that elicit the development of significant mathematical models.     

Understanding How Students Develop Mathematical Models

in this article, we discuss findings from a research study designed to characterize students' development of significant mathematical models by examining the shifts in their thinking that occur during problem investigations. These problem investigations were designed to elicit the development of mathematical models that can be used to describe and explain the relations, patterns, and structure found in data from experienced situations. We were particularly interested in a close examination of the student interactions that appear to foster the development of such mathematical models. This classroom-based qualitative case study was conducted with precalculus students enrolled in a moderate-sized private research university. We observed several groups of 3 students each as they worked together on 5 different modeling tasks. In each task, the students were asked to create a quantitative system that could describe and explain the patterns and structures in an experienced situation and that could be used to make predictions about the situation. Our analysis of the data revealed 4 sources of mismatches that were significant in bringing about the occurrence of shifts in student thinking: conjecturing, questioning, impasses to progress, and the use of technology-based representations. The shifts in thinking in turn led to the development of mathematical models. These results suggest that students would benefit from learning environments that provide them with ample opportunity to express their ideas, ask questions, make reasoned guesses, and work with technology while engaging in problem situations that elicit the development of significant mathematical models.     

数学模型在高校领军人才评审中的应用

教育评估的可靠性决定了评估结果的可信性,影响着教育评估的声誉和发展.结合高校领军人才评审探讨了数学可靠性模型在教育评估中的应用,通过建立数学可靠性模型,计算评审系统的可靠性,并结合可靠性计算结果分析了影响评审系统可靠性的因素.     

一种求解救灾物资运输问题的改进解法

本文通过对B运输问题建立数学模型,提出了一种求解B运输问题的改进解法。改进解法首先通过最小元素法求出初始解,然后进行变量闭回路法调整,直到求出最优解,并给出了一个计算实例证明了解法的有效性。文章还对改进解法和另外两种现有的算法进行了综合的分析,由于改进解法计算过程中采用的变量闭回路法省略了求检验数的环节,使得新算法比两种现有的算法更简便。     

人才评价与选拔的一种模型及应用

为了客观公正地评价与选拔人才，本在实践经验总结的基础上，采用定量的数学计算和定性的评价分析相结合的方式，对人才评价与选拔给出了一种数学模型，并用实例说明了模型的应用。     

Predictive factors of students’ motivation to succeed in introductory mathematics courses: evidence from higher education in the UAE

The purpose of the study is to examine whether there is a significant relationship between students’ motivation to succeed in introductory mathematics courses offered by universities in the United Arab Emirates (UAE) as the dependent variable of the research and another five independent variables including cognitive mathematics self-concept, affective mathematics self-concept, extrinsic motivation as expectations of future career and income, students’ age and the number of mathematics courses taken by students. The rationale of the study is based on the significance of mathematics achievements for students and academic institutions in particular, as well as for the society in general. The study is designed based on a quantitative research methodology and a sample of 685 students participated in completing a survey questionnaire. The sample is drawn from students who were registered in different introductory mathematics courses at four academic institutions of higher education in the UAE. The quantitative correlation analysis among students’ motivation, cognitive mathematics self-concept, affective mathematics self-concept, extrinsic motivation, students’ age and the number of mathematics courses taken by students reveals theoretically consistent interrelationships. The quantitative multiple regression analysis indicates that the five independent variables explain 71.3% of the variation in students’ motivation to succeed in introductory mathematics courses.     

考虑公司信息披露情绪的欧式脆弱期权定价

从公司信息披露的角度来看,定量数据直观地反映了公司的经营和财务状况,而描述性的非结构文本信息是对定量数据的有效补充。本文从公司年报中挖掘信用违约文本信息,构建语调变量情绪指标,以调控脆弱期权的违约临界值,改进经典的Klein欧式脆弱期权定价模型。研究表明:随着语调变量指标的增大,欧式看涨看跌期权价格呈递减趋势,且指标越接近1,期权价格递减速度越快,说明期权价格对负向情绪更加敏感,符合金融市场实际情况。此外,应用研究发现不考虑情绪指标的Klein模型倾向于低估期权价格,考虑公司信息披露情绪的脆弱期权定价模型能更准确地分析财务困境对信用风险的影响,结果更贴近实际情况。     

Students Explaining Solutions in Student-Directed Groups: Cooperative Learning and Reform in Mathematics Education

Cooperative learning experiences can contribute to mathematics education reform by stimulating student communication. Sixth grade student conversations were recorded on four occasions over a four month period when they were working in cooperative groups. The results indicated that routine compliance with the requirement to “explain” superseded authentic dialogues about mathematical ideas. Student conversations were influenced by the model of explanation exchanges emerging from the teacher's visits to groups. Teacher influence was mediated by students' past experiences. The findings suggest that teachers implementing reform should help students develop criteria for judging mathematical arguments and confront student conceptions directly to deepen debates.     

Bringing brain imaging to the school to assess arithmetic problem solving: chances and limitations in combining educational and neuroscientific research

Scientific collaboration between neuroscience and mathematics education has mostly focused on brain imaging trying to inform education. This study aims at meeting expectations of both research fields, thus enhancing the ecological validity. We investigated the influence of age, mathematical competency, and task characteristics (format, complexity) on students’ arithmetic performance. Based on behavioral data from a pilot study (n = 73), arithmetic tasks were chosen for a subsequent investigation (n = 90), in which parietal brain activation was measured with near-infrared spectroscopy. Substantial group differences in calculation time were observed. While task characteristics influenced arithmetic performance in both age groups, this influence was much smaller for grade 8 students. However, parietal brain activation during calculation was not affected by age, mathematical competency, or task characteristics. Limitations of the experimental design and general problems of applying imaging methods to the school context are discussed.