Theory of statistical inference

统计推断理论

• 批准号: RGPIN-2020-05897
• 负责人: Reid, Nancy
• 金额: $ 3.13万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2021
• 资助国家: 加拿大
• 起止时间: 2021-01-01 至 2022-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=740901
• 关键词: Theory; statistical; inference

Modern technology has simplified the collection of large and complex sets of data, which are being used to answer important research questions in many fields of science and engineering.  Statistical models and methods are an essential part of this research, and understanding these methods requires progress on the theory of statistical modelling and inference. The proposed research program is intended to deepen our understanding of the intellectual foundations of the field of statistics and to provide a framework for developing new methods of analysis. Research in statistical theory looks for commonalities underlying a wide range of scientific problems. The feedback cycle between theory and applications of statistical science is one of the most interesting and important aspects of the subject. Particular emphasis will be placed on developing methods of inference based on the likelihood function, as this has a central role in Bayesian and frequentist approaches to inference.  There continues to be an ongoing debate about the use of these different modes of inference in scientific advances. Careful study of the basic principles of statistical inference can help to inform this debate.  This research program also emphasizes the study of mathematical properties of inference methods using asymptotic expansions, a technique that studies how methods depend on the size of the data set being analysed.  With infinite amounts of data, Bayesian and frequentist methods agree, but it turns out that their disagreement in finite samples can be pinpointed with the help of asymptotic expansions.   In the current technological landscape, the amount of data available to scientists and engineers is nearly unlimited, but as the size of a set of data increases, so does the complexity of the mathematical models used to help us understand the structure in the data.  These models are used to summarize key features of a problem, to shed light on scientific hypotheses under study, and to make predictions for what we might expect to see in similar circumstances.  When the models become very complex, and in particular involve very large numbers of parameters, relative to the number of observations we can collect, new theory is needed to inform for statistical summaries, inferences and predictions. A major focus of this research program is contributing to these developments.  Data that is very large, and/or complex, is often used to design algorithms that give good predictions; this is the focus of much work in machine learning and some branches of artificial intelligence. Statistical best practices around the collection, and protection, of data can be very useful in assessing the reliability of these methods for widespread use in the population. Statistical concepts relevant to inference can also be very useful to advance the explainability of these algorithms. This  research program will emphasize the importance of statistical thinking in learning from data.

现代技术简化了大型复杂数据的收集，这些数据被用来回答许多科学和工程领域的重要研究问题。  统计模型和方法是这项研究的重要组成部分，理解这些方法需要统计建模和推理理论的进展。拟议的研究计划旨在加深我们对统计领域知识基础的理解，并为开发新的分析方法提供框架。统计理论研究寻找各种科学问题背后的共性。统计科学的理论和应用之间的反馈循环是该学科最有趣和最重要的方面之一。将特别强调开发基于似然函数的推理方法，因为这在贝叶斯和频率主义推理方法中起着核心作用。  关于在科学进步中使用这些不同的推理模式仍然存在持续的争论。仔细研究统计推断的基本原理有助于为这场辩论提供信息。  该研究计划还强调使用渐近展开来研究推理方法的数学特性，渐近展开是一种研究方法如何依赖于所分析数据集大小的技术。  对于无限量的数据，贝叶斯方法和频率论方法是一致的，但事实证明，它们在有限样本中的分歧可以借助渐近展开来查明。   在当前的技术领域，科学家和工程师可以获得的数据量几乎是无限的，但随着数据集规模的增加，用于帮助我们理解数据结构的数学模型的复杂性也随之增加。  这些模型用于总结问题的关键特征，阐明正在研究的科学假设，并预测我们在类似情况下可能会看到的情况。  当模型变得非常复杂，特别是涉及相对于我们可以收集的观察数量而言非常大量的参数时，就需要新的理论来为统计总结、推论和预测提供信息。该研究计划的一个主要重点是促进这些发展。  非常大和/或复杂的数据通常用于设计能够提供良好预测的算法；这是机器学习和人工智能的一些分支中许多工作的重点。围绕数据收集和保护的统计最佳实践对于评估这些方法在人群中广泛使用的可靠性非常有用。与推理相关的统计概念对于提高这些算法的可解释性也非常有用。 该研究计划将强调统计思维在从数据中学习的重要性。