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: 1007520
• 负责人: Thomas Chun Man Lee
• 金额: $ 12.5万
• 依托单位: University of California-Davis
• 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=1007520&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.

该提案的动机是广义基准推理的成功，该推理由 PI 引入，作为费舍尔基准论证的概括。 PI 对广义基准方法的理论和应用进行了大量研究，得出以下重要结论： (a) 可以使用统一和系统的程序来为大类问题开发基准解决方案； (b) 基准方法通常会产生非常有效的推理程序，因此与使用其他方法开发的程序相比具有竞争力； (c) 基准程序在大类问题中是渐近正确的； (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，这表明这两种方法通常并不等效； (e) 贝叶斯方法和基准方法都产生了有用的区间推理程序，正如这两个领域的各种出版物中所建立的那样。显然，这两种方法都不能声称主导另一种方法。 (f) 两种方法通常都需要针对所需后验或基准分布的实际数值计算进行 MCMC 模拟。在适当考虑了基准方法有望在理论和实践方面产生新的有用结果的统计推断领域后，首席研究员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) 扩展 PI 的工作，以解决广义基准推理框架内的模型选择问题； (c) 参数稳健基准分布概念的定义和研究以及根据数据计算该分布的计算方法的开发； (d) 在一些标准参数示例中应用稳健基准方法以得出新的稳健推理方法； (e) 开发一些通用计算策略，以实现复杂实际问题的基准方法。该提案研究了一种基于费舍尔基准论证的统计推断新方法。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) 指导文件详细说明了证明两种或多种药物配方等效性的分析程序。 PI 旨在表明基准方法将带来更高效的程序，从而节省成本和时间，这对制药行业来说是一个重要问题。在计量领域，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)，其中给出了美国 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，每次测量都会受到未知和不可知的系统误差的影响，这些误差通常大于随机误差。目前唯一已知的量化这些不可知的系统误差的方法是通过指定它们的主观分布。 GUM 指定了一些临时方法，用于将某些误差分量的标准偏差的基于数据的估计与其他误差分量的不确定性的主观估计相结合。 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当前程序。