Statistical Modelling and Inference with Complex Data

从自然科学到工程学，从健康科学到人文科学和社会科学，各个领域的研究都大大受益于统计科学。然而，构成流行统计软件包中实施的大多数技术的许多常用推理程序假定数据是理论上理想的格式，例如，独立和相同分布的观察值的集合。不幸的是，这一假设在现实生活研究中往往不现实，因此对输出的传统解释可能会产生误导。一些研究人员注意到，其数据的复杂结构使现有统计工具失效，但他们没有替代办法。*这一拟议研究方案的广泛目标是开发统计建模和推断的新方法，以绕过复杂数据背景下传统统计工具的挑战和限制。我们的三个重点是效率、健壮性和可行性。这项建议的具体目标是：(1)利用现成的纵向信息为粗化事件时间提出新的模型和方法；(2)在协变量信息不完全的情况下，研究具有时间依赖协变量的回归分析；以及(3)为接受信息检验的纵向观测开发新的公式和分析程序。所有统计问题都是根据现实生活中的项目制定的；将制定专门的程序，以解决应用中的特殊挑战。统计模型是一种强大的工具，为研究人员提供了对复杂系统的深入了解和预测能力。采用我最近在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来建立相关模型并进行具有科学意义的分析。*培训总部医生和传播研究成果是拟议研究的两个重要方面。学生将参与整个研究活动，包括文献回顾、统计公式、渐近推导、模拟和实际数据分析。我们将开发软件包，以便在研究足够成熟时，使统计从业者能够获得这些研究。我们预计，拟议的研究将通过提供可行、有效和可靠的方法，为统计理论和实践作出贡献，相关培训将培养出高素质的统计人员。

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.**