Mathematical Sciences: Models and Methodology for Positive Dependence

数学科学：正依赖的模型和方法

• 批准号: 9203444
• 负责人: Henry Block
• 金额: $ 9万
• 依托单位: University of Pittsburgh
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-07-15 至 1994-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9203444&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Models; Methodology; Positive

Within the framework of positive dependence and reliability theory, a number of major research topics in statistics and applied probability modeling are proposed. These include: (a) development of the statistical applications of metrics and related orderings on permutations; (b) new and more efficient isotonic regression algorithms for partially ordered spaces; and (c) various techniques for types of ordinal data analyses. Additional topics include reliability maintenance models, models and methodology for random length multivariate normal data, and combinatoric identities arising from nonhomogeneous Poisson processes. The research approaches to these topics employ results and techniques from positive dependence, reliability theory and multivariate analysis. The principal investigators will explore a number of theoretical topics in the area of multivariate statistical analysis called positive dependence and consider a number of applications of these theoretical results. In particular the investigators plan to develop new computational algorithms that are more efficient than current algorithms. The purpose of this research is to develop strategies for maintaining a system in an optimal fashion balancing the cost of maintenance against the cost of break-downs.

在正相关性和可靠性理论的框架内，提出了统计学和应用概率建模的一些重大研究课题。这些包括：(a)发展度量和有关排列排序的统计应用；(b)新的更有效的偏序空间等压回归算法；(c)各种类型的有序数据分析技术。其他主题包括可靠性维护模型，随机长度多元正态数据的模型和方法，以及由非齐次泊松过程产生的组合恒等式。这些课题的研究方法采用了正相关性、可靠性理论和多变量分析的结果和技术。主要研究人员将探索多元统计分析领域的一些理论主题，称为积极依赖，并考虑这些理论结果的一些应用。特别是，研究人员计划开发比现有算法更有效的新计算算法。本研究的目的是制定策略，以最佳方式维护系统，平衡维护成本和故障成本。