Mathematical Sciences: Principles and Practices of Applied Statistics

该项目旨在跟进国家科学基金会赠款DMS-90-03216(数据分析、建模和推理)下开展的项目，并启动和开展与前一笔赠款相同类型的研究。这些项目有两种基本类型。第一类力求在若干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(主要是贝叶斯推理)。这些项目包括估计州一级就业率和失业率的研究、关于血浆中激素浓度动态模式的建模和推断、对医院ICU以及其他社会、环境或地球物理过程的研究。第二种基本类型的研究是方法论问题的理论分析，包括了解和改进面对低频时间序列行为的统计方法，处理模型选择的逻辑，研究加权抽样下的设计和分析问题，研究信念函数推理的合理性和计算，以及追溯20世纪统计学中有争议的问题的历史，主要集中在概率推理上。统计研究是物理、生物和社会科学几乎每一个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，很大程度上是因为计算机使收集和分析大量信息成为可能，也使管理统计现象的数学理论和规律的研究发生了革命性的变化。因此，开发和评估统计科学家所依赖的方法来理解数据，并将他们的发现打包用于实际目的，例如评估全球变暖的长期趋势，帮助医生做出正确的医疗决策，或者为政府政策制定者提供准确和及时的经济信息，是一种持续且日益增长的需要。该项目采取的一项基本战略是，应在具体科学问题的框架内开发技术工具，并通过与积极致力于这些问题的科学家的合作努力，以保证所开发的程序和模型的相关性。此外，由于统计方法具有在非常不同的科学领域中具有共性的特征，因此必须寻求第二种战略来解决和改进在这些不同领域中以相同形式出现的问题。在统计学上，这些问题围绕着应对有关测量的不确定性，或关于可能在不确定知识基础上做出的决定的后果。该项目通过依赖于概率数学理论的技术来解决这些问题。重要的是提炼和阐明指导选择和使用此类数学的原则和技术。

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.