Collaborative Research: Generalized Fiducial Inference - An Emerging View

协作研究：广义基准推理 - 一种新兴观点

• 批准号: 1007543
• 负责人: Jan Hannig
• 金额: $ 12.5万
• 依托单位: University of North Carolina at Chapel Hill
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-09-01 至 2014-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1007543&HistoricalAwards=false
• 关键词: Collaborative; Research; Generalized; Fiducial; Inference

This proposal is motivated by the success of Generalized Fiducial Inference as introduced by the PIs as a generalization of Fisher's fiducial argument. As a result of the many studies conducted by the PIs on the theory and applications of generalized fiducial methods the following important conclusions can be made: (a) A unified and systematic procedure is available for developing fiducial solutions for large classes of problems; (b) The fiducial approach generally leads to very efficient inference procedures and thus they are competitive with procedures developed using other approaches; (c) Fiducial procedures are asymptotically correct in large classes of problems; (d) Many fiducial distributions can also be realized as a Bayesian posterior by an appropriate choice of a prior. However, this is not always possible, which establishes that the two approaches are not equivalent in general; (e) Both the Bayesian approach and the fiducial approach lead to useful interval inference procedures as have been established in various publications in both areas. It is clear that neither approach can claim to dominate the other; (f) Both approaches typically require MCMC simulations in regards to actual numerical computation of the required posterior or fiducial distributions. After giving due consideration to areas of statistical inference where a fiducial approach is expected to lead to new and useful results, both theoretical and practical, the PIs propose to conduct research into the following topics: (a) Extensions of Interval Data fiducial framework for Generalized Linear Mixed Models together with associated computational approaches; (b) Extension of the work of the PIs to address the model selection problem within the Generalized Fiducial Inference framework; (c) Definition and investigation of the concept of a Robustified Fiducial Distribution for a parameter and development of computational methods for calculating it from data; (d) Application of robust fiducial approaches to arrive at new robust inference methods in some standard parametric examples; (e) Development of some general computational strategies for implementation of fiducial methods for complex practical problems.This proposal studies a new approach to statistical inference based on Fisher's fiducial argument. The implications of this work will have an immediate effect on public policy. For instance, the U.S. Food and Drug Administration (FDA) guidance document spells out analysis procedures for demonstration of equivalence of two or more drug formulations. The PIs aim to show that the fiducial approach will lead to more efficient procedures, which will result in cost and time savings, an important issue for the drug industry. In metrology, the International Bureau of Weights and Measures (BIPM) in conjunction with the International Organization for Standardization (ISO), has published a ``Guide to Expression of Uncertainty in Measurements'' (GUM) which gives the procedures to be followed by national metrological institutes such as NIST in the US, NPL in UK, and PTB in Germany. A problem that is unique to metrology is that every measurement is subject to unknown and unknowable systematic errors that are often larger than random errors. The only currently known way to quantify these unknowable systematic errors is via specification of subjective distributions for them. The GUM specifies some ad hoc methods for combining data-based estimates of standard deviations for some error components and subjective estimates of uncertainty for other error components. The PIs aim to demonstrate that the fiducial method provides a new natural approach for accomplishing this. Such results are likely to influence the metrology community in modifying and improving their current procedures.

这一提议的动机是由pi作为费雪的基准论证的推广而引入的广义基准推理的成功。由于pi对广义基准方法的理论和应用进行了许多研究，可以得出以下重要结论：(a)有一个统一和系统的程序可用于为大类问题制定基准解；(b)基准方法通常导致非常有效的推理程序，因此它们与使用其他方法制定的程序具有竞争力；(c)基准程序在大量问题中是渐近正确的；(d)许多基准分布也可以通过适当选择先验来实现贝叶斯后验。然而，这并不总是可能的，这确定了这两种方法在一般情况下是不等同的；(e)贝叶斯方法和基准方法都能产生有用的区间推断程序，这在这两个领域的各种出版物中都已确立。很明显，两种方法都不能声称支配对方；(f)这两种方法通常都需要MCMC模拟，以便对所需的后验分布或基准分布进行实际数值计算。在适当考虑了基准方法有望在理论和实践中产生新的有用结果的统计推断领域之后，pi建议对以下主题进行研究：(a)广义线性混合模型的区间数据基准框架的扩展以及相关的计算方法；(b)扩大pi的工作，以便在广义基准推理框架内解决模型选择问题；(c)定义和研究参数的稳健基准分布概念，并发展从数据计算参数的计算方法；(d)在一些标准参数例子中应用鲁棒基准方法得出新的鲁棒推理方法；(e)为执行复杂实际问题的基本方法制订一些一般计算策略。本文在费雪的基准论证的基础上，研究了一种新的统计推断方法。这项工作的影响将对公共政策产生直接影响。例如，美国食品和药物管理局（FDA）的指导文件详细说明了证明两种或两种以上药物配方等效性的分析程序。PIs旨在表明，基准方法将导致更有效的程序，从而节省成本和时间，这是制药业的一个重要问题。在计量方面，国际计量局（BIPM）与国际标准化组织（ISO）联合发布了“测量不确定度表达指南”（GUM），该指南给出了美国NIST、英国NPL和德国PTB等国家计量机构应遵循的程序。计量学特有的一个问题是，每次测量都受到未知和不可知的系统误差的影响，这些误差往往大于随机误差。目前唯一已知的量化这些不可知的系统误差的方法是对它们的主观分布进行规范。GUM指定了一些特别的方法，用于结合对某些误差分量的基于数据的标准偏差估计和对其他误差分量的不确定性的主观估计。实验的目的是证明基准方法为实现这一目标提供了一种新的自然方法。这样的结果可能会影响计量界修改和改进他们目前的程序。