Mathematical Sciences: Application of Interval Analysis in Statistical Computing

数学科学：区间分析在统计计算中的应用

• 批准号: 9500831
• 负责人: William Kennedy
• 金额: $ 5万
• 依托单位: Iowa State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9500831&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Application; Interval; Analysis

9500831 Kennedy Abstract The IEEE proposed standard for binary floating-point computer arithmetic has been adopted by most computer manufacturers. Included among the features of this floating-point number system is programmer selectable rounding mode. Two rounding modes, round to plus or minus infinity, give hardware support for implementations of interval analysis computations. Substantive areas outside statistics are employing interval analysis and interval computations to good advantage in research. Research workers in statistical computing have been slow to recognize or evaluate the potential utility of interval analysis. The overall objective of this research is to identify areas in statistical computing where interval analysis can be used to good advantage, and to develop needed methods and algorithms in these areas. Specifically, a library of routines for self- validating approximation of cdf and inverse cdf for most of the usual univariate continuous probability distributions, and selected multivariate distributions will be developed. Accuracy essentially to machine precision over very broad areas of the variable/parameter space will be the goal. Self-validating computational methods for certain kinds of global optimization problems will also be developed. Scientific computations are usually done using a digital computer. Computers are not, however, capable of expressing exactly most numbers that constitute intermediate and final results for a computing problem. A part of the inexactness inherent in computer arithmetic is due to the need to round to a specific number of numeric digits after each arithmetic operation. Therefore answers produced by a computer for difficult computing tasks are often only rough approximations to the unknown true answers which would be obtained if exact computations could be performed. The objective of this research project is to develop alternative computational methods that yield more accurate answers in difficult statistical computing ap plications. The price of increased accuracy is that substantially more computer resources are consumed to produce answers. However, today there are enough computer resources available to support this very computationally intensive approach. The main motivation for the research is that it is best to spend extra time and effort to insure good answers, instead of settling for poor answers that are obtained quickly.

9500831肯尼迪摘要 IEEE提出的二进制浮点计算机算法标准已被大多数计算机制造商采用。 该浮点数系统的特性包括程序员可选择的舍入模式。两种舍入模式，舍入到正无穷大或负无穷大，为区间分析计算的实现提供了硬件支持。统计学之外的实质性领域正在使用区间分析和区间计算来进行研究。 统计计算领域的研究人员对区间分析的潜在效用的认识和评估一直很慢。 本研究的总体目标是确定在统计计算领域的区间分析可以使用到很好的优势，并在这些领域开发所需的方法和算法。具体来说，将开发一个程序库，用于对大多数常见的单变量连续概率分布和选定的多变量分布进行cdf和cdf逆的自验证近似。目标是在变量/参数空间的非常广泛的区域内实现基本上达到机器精度的精度。 还将开发用于某些类型的全局优化问题的自验证计算方法。 科学计算通常是用数字计算机完成的。然而，计算机不能精确地表达构成计算问题的中间和最终结果的大多数数字。计算机算术中固有的不精确性的一部分是由于每次算术运算后需要舍入到特定的数字位数。 因此，由计算机为困难的计算任务所产生的答案通常只是对未知的真实答案的粗略近似，如果可以进行精确计算，则可以获得未知的真实答案。这个研究项目的目标是开发替代的计算方法，在困难的统计计算应用中产生更准确的答案。提高准确性的代价是消耗更多的计算机资源来产生答案。然而，今天有足够的计算机资源可用于支持这种非常计算密集的方法。这项研究的主要动机是，最好花额外的时间和精力来确保好的答案，而不是解决快速获得的糟糕答案。