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.

该提议是由PIS引入的普遍信托学推断的成功所激发的，这是Fisher的基准论证的普遍性。由于PI对广义基准方法的理论和应用进行的许多研究可以得出以下重要结论：（a）可以针对大量问题开发基准解决方案的统一和系统的程序； （b）基准方法通常会导致非常有效的推理程序，因此它们与使用其他方法开发的程序具有竞争力； （c）基准程序在大量问题中渐近正确； （d）许多基准分布也可以通过适当的先验选择来实现为贝叶斯后部。但是，这并不总是可能的，这表明两种方法一般都不相等。 （e）贝叶斯的方法和基准方法都导致有用的间隔推断程序，这在这两个领域的各个出版物中都建立了。显然，两种方法都不能声称统治对方。 （f）两种方法通常都需要MCMC模拟，以实现所需后或基准分布的实际数值计算。在对统计推断领域进行了适当考虑，预计基准方法会导致理论和实用性的新成果，PIS提议对以下主题进行研究：（a）间隔数据信托框架的扩展，用于广义线性混合模型以及相关计算方法的广义线性混合模型； （b）扩展PI在广义基金推理框架内解决模型选择问题的工作； （c）对参数的鲁棒性基准分布的概念的定义和调查，用于从数据中计算出来的计算方法； （d）在某些标准参数示例中采用强大的信托方法来达到新的鲁棒推理方法； （e）开发一些用于实施复杂实际问题的基准方法的一般计算策略。该提案研究基于费舍尔的信托论点的一种新的统计推断方法。这项工作的含义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）指导文件阐明了分析程序，以证明两种或多种药物配方的等效性。 PI的目的是表明基准方法将导致更有效的程序，这将导致成本和时间节省，这对药品行业来说是一个重要的问题。在计量学上，国际重量与措施局（BIPM）与国际标准化组织（ISO）结合使用，已发布``测量中的不确定性表达指南''（GUM）'（GUM）提供了程序，该程序遵循了由国家中的NPLING NPLING NPLING in UK和PTB的NPLIST和PTB。一个是计量学独有的问题是，每个测量值都受到通常比随机误差大的未知和不可知的系统错误。量化这些不可知的系统错误的唯一已知方法是通过为它们的主观分布进行规范。口香糖指定了一些临时方法，用于结合某些错误组件的基于数据的标准偏差的估计以及其他错误组件的不确定性的主观估计。 PI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社区，以修改和改善其当前程序。