Statistical Modelling and Inference with Complex Data

从自然科学到工程学、卫生科学、人文科学和社会科学等领域的研究都极大地受益于统计科学。然而，许多常用的推断程序（在流行的统计软件包中构成了大多数技术）假设数据是理论上理想的格式，例如，独立和相同分布的观测值的集合。不幸的是，这种假设在现实生活的研究中往往是不现实的，因此对输出的传统解释可能会产生误导。一些研究人员观察到，他们的数据结构复杂，使现有的统计工具失效，但他们没有其他方法。***本研究计划的主要目标是开发统计建模和推理的新方法，以规避传统统计工具在复杂数据背景下的挑战和局限性。我们的三个重点是效率、健壮性和可行性。本提案的具体目标是：(1)利用现成的纵向信息提出粗化事件时间的新模型和方法；(2)在协变量信息不完整的情况下，研究含时变协变量的回归分析；(3)制定新的纵向观测数据的制定和分析程序，以进行信息检验。所有的统计问题都是基于现实项目制定的；将制定专门的程序来解决应用程序中的特殊挑战。统计模型是一种强大的工具，它为研究人员提供了对复杂系统的深刻理解和做出预测的能力。根据我最近在nserc资助的研究项目中开发的框架，我们将利用应用领域的信息建立相关模型并进行有科学意义的分析。***培训hqp和传播研究成果是拟议研究的两个重要方面。学生将参与整个范围的研究活动，包括文献综述、统计公式、渐近推导、模拟和实际数据分析。当研究足够成熟时，我们将开发软件包，使统计从业者可以访问研究。我们预计，拟议的研究将通过提供可行、有效和稳健的方法，为统计理论和实践做出贡献，并且相关的培训将培养出高素质的统计学家

Studies in fields ranging from natural sciences to engineering to health sciences to human and social sciences have benefited greatly from the statistical sciences. However, many commonly used inferential procedures, which form the majority of the techniques implemented in popular statistical software packages, assume that the data are in a theoretically ideal format, e.g., a collection of independent and identically distributed observations. Unfortunately, this assumption is often not realistic in real-life studies, and thus conventional interpretations of the output can be misleading. Some researchers have observed that the complex structures of their data invalidate existing statistical tools, but they do not have alternative approaches.***The broad objective of this proposed research program is to develop new methodology for statistical modelling and inference to circumvent the challenges and limitations of conventional statistical tools in the context of complex data. Our three focal points are efficiency, robustness, and feasibility. The specific aims of this proposal are (1) to propose new models and approaches for coarsened event times using readily available longitudinal information; (2) to investigate regression analysis with time-dependent covariates in the presence of incomplete covariate information; and (3) to develop new formulation and analysis procedures for longitudinal observations subject to informative inspection. All the statistical problems are formulated based on real-life projects; specialized procedures will be developed to address particular challenges in applications. Statistical models are powerful tools that offer researchers a deep understanding of complex systems and the ability to make predictions. Adapting the framework developed in my recent NSERC-funded research program, we will utilize information from application areas to build relevant models and conduct scientifically meaningful analyses. ***Training HQPs and disseminating the research results are two important aspects of the proposed research. Students will participate in the whole range of research activities including the literature review, statistical formulation, asymptotic derivation, simulation, and practical data analysis. We will develop software packages to make the research accessible to statistical practitioners when the research is sufficiently mature. We anticipate that the proposed research will contribute to statistical theory and practice by providing feasible, efficient, and robust approaches, and that the associated training will produce highly qualified statisticians.**