Mathematical Sciences: Flowgraph and Saddlepoint Methods for Statistics

数学科学：统计流程图和鞍点方法

• 批准号: 9625672
• 负责人: Aparna Huzurbazar
• 金额: $ 6.9万
• 依托单位: University of New Mexico
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-08-01 至 1999-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9625672&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Flowgraph; Saddlepoint; Methods

DMS 9625672 Huzurbazar This research involves the application of flowgraph and saddlepoint methods to problems in statistics with particular emphasis on prediction in stochastic networks. Stochastic network models are of current interest in statistics and can be applied to study a variety of natural phenomena. Consider the progression of diseases such as kidney failure, cancer, or AIDS. Of interest is the prediction of a survival time for a patient. Survival times can be thought of as first passage times from one state to another in a stochastic network so that prediction of a survival time for a patient involves analysis of a complex stochastic network. This research is concerned with such prediction. Methodology is developed for computation of Bayesian predictive distributions for stochastic networks in situations involving a multitude of covariates and heavily censored data. These methods are used in conjunction with generalized linear models and proportional hazards models, so that predictive distributions as well as predictive hazards and predictive survival functions for first passage times between any two states of a disease, or more generally, stochastic networks, are computed. %%% This is a study of flowgraphs which extends beyond the natural emphasis area of survival analysis into several diverse areas of engineering systems. Flowgraphs were originally developed in the engineering sciences to design and analyze complex systems. For example, these systems could be descriptions of a manufacturing process, the reliability of an artificial organ, or the predicted time to completion of a building project. The analysis of flowgraphs traditionally has been hampered by computational difficulties. Current engineering methods involve time-consuming computer simulations. The computational aspects of this research are based on saddlepoint approximations. Saddlepoint approximations are high performance computationally intensive techniques that provid e fast and accurate approximations to these problems. The results developed here are applicable in the areas of reliability, and industrial, electrical, and systems engineering, in addition to survival analysis. ***

DMS 9625672 Huzurbazar 这项研究涉及应用流图和鞍点方法的问题，特别强调在随机网络的预测统计。随机网络模型是当前研究的热点 它可以应用于研究各种自然现象。 考虑疾病的进展，如肾衰竭，癌症或艾滋病。感兴趣的是预测患者的存活时间。 生存时间可以被认为是随机网络中从一个状态到另一个状态的第一次通过时间，因此对患者生存时间的预测涉及复杂随机网络的分析。本研究就是针对这种预测。 研究了随机网络中涉及大量协变量和严重删失数据的贝叶斯预测分布的计算方法。 这些方法与广义线性模型结合使用 和比例风险模型，因此预测分布以及 预测危险和预测生存功能， 计算疾病或更一般地随机网络的任何两个状态之间的首次通过时间。 %%% 这是一个流程图的研究， 自然的重点领域的生存分析到几个不同领域的工程系统。 流程图最初是在工程科学中开发的，用于设计和分析复杂系统。例如，这些系统可以是 制造过程的描述，人造器官的可靠性，或建筑项目的预计完工时间。传统的流程图分析一直受到计算困难的阻碍。当前工程方法 涉及耗时的计算机模拟。这项研究的计算方面是基于鞍点近似。 鞍点近似是高性能的计算密集型 这些技术为这些问题提供了快速和准确的近似。 这里开发的结果适用于可靠性领域， 工业，电气和系统工程，以及生存分析。 ***