Mathematical Sciences: Principles and Practices of Applied Statistics

数学科学：应用统计学原理与实践

• 批准号: 9404396
• 负责人: Arthur Dempster
• 金额: $ 28.11万
• 依托单位: Harvard University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-01 至 1999-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9404396&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Principles; Practices; Applied

The project is designed to follow up projects carried out under NSF Grant DMS-90-03216 (Data Analysis, Modelling, and Inference) and to intitiate and carry out research of the same types as under the previous grant. These projects are of two basic types. The first type seeks to develop new statistical techniques in the context of several case studies, with the goal of integrating tools of various sorts, including study design, data analysis, modelling, and inference (mainly Bayesian inference). The projects includeJ a study of estimating state level employment and unemployment rates, modelling and inference concerning dynamic patterns of hormone concentrations in blood plasma, a study of hospital ICUs, and other social , environmental or geophysical processes. The second basic type of study is theoretical analysis of methodological issues, including understanding and improving statistical methods in the face of low frequency time series behavior, addressing the logic of model selection, studying design and analysis issues under weighted sampling, studying the justification and computation of belief function inferences, and tracing the history of contentious issues in 20th century statistics, mostly centering on probabilistic inference. Statistical studies are essential contributors to scientific knowledge in virtually every branch of physical, biological, and social sciences. The nature of these studies is changing rapidly, in large part because computers have made possible the collection and analysis of large quantities of information, and also have revolutionized the study of the mathematical theories and laws that govern statistical phenomena. Consequently, there is a continuing and growing need to develop and assess the methods that statistical scientists rely upon to make sense of data and to package their findings for practical purposes, such as assessing long term trends in global warming, aiding doctors to make good decisions about medical treatments, or providing accurate and timely information about the economy for government poicymakers. A basic strategy adopted in the project is that technical tools should be developed in the framework of specific scientific problems, and through collaborative efforts with scientists actively working on such problems, in order to guarantee the relevance of the procedures and models developed. Also, since statistical methodology has features that are shared in common across very different fields of science, it is important to pursue a second strategy of addressing and improving problems that arise in the same form in these different fields. In statistics, these problems center around coping with uncertainties about measurements or about the consequences of decisions that might be taken on the basis of uncertain knowledge. The project addresses such problems through techniques that rely on the mathematical theory of probability. It is important to refine and clarify the principles and techniques that govern the selection and use of such mathematics.

该项目旨在跟进根据NSF Grant DMS-90-03216（数据分析，建模和推理）进行的项目，并对与上一笔赠款相同的类型进行促进和进行研究。这些项目是两种基本类型。 第一类试图在几个案例研究的背景下开发新的统计技术，目的是整合各种工具，包括研究设计，数据分析，建模和推理（主要是贝叶斯推论）。这些项目包括一项研究估计州级就业和失业率的研究，关于血浆中激素浓度的动态模式的建模和推理，对医院ICU的研究以及其他社会，环境或地球物理过程。第二种基本类型的研究是对方法论问题的理论分析，包括面对低频时间序列行为的理解和改进统计方法，解决模型选择的逻辑，研究加权采样下的设计和分析问题，研究信仰功能推断的合理性和计算，以及追溯20世纪统计学中有争议问题的历史，以概率为基础，以概率为基础。 统计研究是几乎每个物理，生物学和社会科学分支的科学知识的重要贡献者。这些研究的性质正在迅速变化，这在很大程度上是因为计算机使大量信息的收集和分析成为可能，并且也彻底改变了对控制统计现象的数学理论和法律的研究。因此，统计科学家所依赖的方法持续且不断增长的需求是为了理解数据并为实际目的打包他们的发现，例如评估全球变暖的长期趋势，帮助医生对医疗治疗做出良好的决定，或为政府Poicymakers提供有关经济的准确和及时的信息。该项目采用的基本策略是，应在特定科学问题的框架内开发技术工具，并通过与科学家积极研究此类问题的合作，以确保开发的程序和模型的相关性。 同样，由于统计方法论具有在非常不同的科学领域共有共同的特征，因此采取第二种策略来解决和改善这些不同领域中相同形式出现的问题。 在统计数据中，这些问题围绕应对有关测量值的不确定性或根据不确定知识而做出的决策后果的不确定性。该项目通过依赖概率数学理论的技术来解决此类问题。重要的是要完善和阐明控制此类数学选择和使用的原理和技术。