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: 1007542
• 负责人: Hariharan Iyer
• 金额: $ 5万
• 依托单位: Colorado State University
• 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 2013-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1007542&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.

这一建议的动机是成功的广义基准推理介绍了PI作为一个概括的费舍尔的基准参数。作为PI对广义基准方法的理论和应用进行的许多研究的结果，可以得出以下重要结论：（a）一个统一的和系统的程序可用于开发大类问题的基准解决方案：（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开发的程序竞争;（c）在大类问题中，基准程序是渐近正确的;（d）通过适当选择先验，许多基准分布也可以实现为贝叶斯后验。然而，这并不总是可能的，这表明这两种方法一般并不等同;（e）贝叶斯方法和基准方法都导致有用的区间推断程序，正如这两个领域的各种出版物所建立的那样。很明显，这两种方法都不能声称占主导地位;（f）这两种方法通常都需要MCMC模拟，以实际数值计算所需的后验或基准分布。在充分考虑采用基准方法预期会在理论和实际上带来新的有用结果的统计推断范畴后，研究员建议就以下课题进行研究：（a）广义线性混合模型的区间数据基准框架的扩展及相关的计算方法;（B）扩大主要研究员的工作，以解决广义基准推断框架内的模型选择问题;（c）第（1）款定义和研究参数的稳健化基准分布的概念，并发展计算方法，数据;（d）在一些标准参数实例中应用稳健的基准方法，以得出新的稳健的推断方法;（e）为复杂的实际问题制定一些通用的计算策略，以实施基准方法，这项建议研究了一种基于Fisher基准论证的统计推断新方法。这项工作的意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）的指导文件阐明了用于证明两种或多种药物制剂等效性的分析程序。 PI旨在表明，基准方法将导致更有效的程序，这将导致成本和时间的节省，这是制药行业的一个重要问题。在计量学方面，国际计量局（BIPM）与国际标准化组织（ISO）共同出版了一份“测量不确定度表示指南”（GUM），该指南提供了美国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，这些系统误差通常大于随机误差。目前唯一已知的方法来量化这些不可知的系统误差是通过规范的主观分布。GUM规定了一些特定的方法，用于将某些误差分量的标准差的基于数据的估计值与其他误差分量的不确定性的主观估计值相结合。 PI旨在证明基准方法为实现这一目标提供了一种新的自然方法。这些结果可能会影响计量界修改和改进其现行程序。