Theory and Methods of Statistical Inference

统计推断理论与方法

• 批准号: RGPIN-2015-06390
• 负责人: Reid, Nancy
• 金额: $ 2.99万
• 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: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=614121
• 关键词: Theory; Methods; 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 it plays a central role in both Bayesian and frequentist inference.  There continues to be an ongoing debate about the role of these two modes of inference in scientific advances; a very accessible overview of the debate was featured in the New York Times (September 29, 2014). Careful study of the basic principles of statistical inference can help to inform this debate.  My 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 make inferences about 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 particularly involve complex dependencies among measurements, statistical inference faces challenges both computationally and theoretically.  Computationally, we may not be able to construct the likelihood function, and inferentially we may not be able to assess the properties of estimated quantities based on the likelihood function. As a result a number of simplifications of likelihood functions have been designed for particular applications. A major focus of the proposed research program is understanding the theoretical properties of these, thus illuminating how computational needs interact with scientific needs for accurate and efficient inference.

现代技术简化了大量复杂数据集的收集，这些数据集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，了解这些方法需要统计建模和推理理论的进步。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一个框架。统计理论的研究寻找广泛的科学问题的共性。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。 特别强调将放在发展的基础上的似然函数的推理方法，因为它在贝叶斯和频率推理中发挥着核心作用。 关于这两种推理模式在科学进步中的作用，仍有一场持续的辩论;纽约时报（2014年9月29日）对这场辩论进行了非常容易理解的概述。仔细研究统计推断的基本原则有助于为这场辩论提供信息。 我的研究计划还强调使用渐近展开的推理方法的数学特性的研究，这种技术研究方法如何依赖于正在分析的数据集的大小。 对于无限数量的数据，贝叶斯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通过渐近展开的帮助来确定。  在当前的技术环境中，科学家和工程师可用的数据量几乎是无限的，但随着数据集大小的增加，用于帮助我们理解数据结构的数学模型的复杂性也在增加。 这些模型用于总结问题的关键特征，对研究中的科学假设进行推断，并对我们在类似情况下可能看到的情况进行预测。 当模型变得非常复杂，特别是涉及测量之间的复杂依赖关系时，统计推断在计算和理论上都面临挑战。 在计算上，我们可能无法构建似然函数，并且因此我们可能无法基于似然函数评估估计量的属性。因此，许多简化的似然函数已被设计用于特定的应用。拟议的研究计划的一个主要重点是了解这些的理论特性，从而阐明计算需求如何与科学需求相互作用，以进行准确和有效的推理。