Messy Data Modeling and Related Topics

- 建议编号：DMS 9803273 PI： 谢敏格机构： 罗格斯大学项目： 混乱数据建模及相关主题 摘要： 这项研究的主要目的是调查一些 处理混乱的数据集所产生的问题， 科学的许多学科。本研究中的数据违反了 传统的假设，如独立性，同质性， 其他的，在更标准的设置下采用。 六个具体的主题;每个主题至少对应一个 违反了传统的假设，一个混乱的数据集可能会有 一个或多个此类违规行为。根据它们的起源 从两个不同的激励数据集，六个主题中的两个解决 关于分组测试方案（Dorfman，1943）及其变体的问题， 包括模拟假阴性和放松 对个人独立性的假设。其余的题目 研究与建模相关的实践和理论问题 批量处理相关回归数据，开发新的模型和方法 对于异质观测。这些发展不仅将 解决特定类型的问题，而且还激发新的 研究开发更通用的方法。 这项研究开发了统计方法，模型和相关的 理论，以解决问题所产生的建模和分析凌乱 数据，可以在许多科学学科中找到，包括生命科学，环境科学，社会科学，工业和 经济学这些杂乱数据的一个共同特点是， 所有这些都违反了一些传统的模型假设，否则， 采用更标准的设置。杂乱数据的精确建模 可以消除不相关的信息， 潜在的机制;最终有利于预测和决策 制作。虽然在发展方面取得了巨大进展， 既有复杂的统计方法， 在过去的半个世纪中，建模中的许多重要问题 和分析杂乱的数据还有待解决，无论是从实际的 和理论观点。这项研究调查了几个这样的 问题虽然模型和方法是针对 制药行业和环境的具体问题 科学，这些发展将不仅解决特定类型的 问题，但也刺激新的研究，以发展更普遍的 方法论。

----------------------------------------------------------------------- Proposal Number: DMS 9803273 PI: Minge Xie Institution: Rutgers University Project: Messy Data Modeling and Related Topics Abstract: The main objective of this research is to investigate a number of problems arising from dealing with messy data sets that occurred in many disciplines of science. The data studied in this research violate conventional assumptions, such as independence, homogeneity, among others, which are otherwise adopted under more standard settings. Six specific topics are presented; each corresponds to at least one violation of conventional assumptions, and a messy data set may have one or more of these types of violations. According to their origins from two different motivating data sets, two of the six topics address problems on group testing scheme (Dorfman, 1943) and its variants, including issues on modeling false negatives and relaxing the assumption of independence on individuals. The rest of the topics investigate practical and theoretical issues related to modeling batch correlated regression data and develop new models and methods for heterogeneous observations. These developments will not only solve the specific type of problems, but also stimulate new researches to develop more general methodologies. This research develops statistical methodologies, models, and related theories to address issues arising from modeling and analysis of messy data, which can be found in many disciplines of the sciences, including life science, environmental science, social science, industry and economics. A common feature of these messy data is that they all violate some conventional model assumptions, which otherwise are adopted under more standard settings. Accurate modeling of messy data can eliminate irrelevant information and provide better understanding of underlying mechanisms; ultimately benefiting prediction and decision making. Although tremendous progress has been made in development of both sophisticated statistical methodologies and elegant mathematical theories in the past half century, many important problems in modeling and analysis of messy data have yet to be tackled, both from practical and theoretical viewpoints. This research investigates several such problems. Although the models and methodologies are tailored to specific problems in the Pharmaceutical industry and environmental science, these developments will not only solve the specific type of problems, but also stimulate new researches to develop more general methodologies.