Collaborative Research: Emerging Variants of Generalized Fiducial Inference

基准推理是进行统计推理的另一种框架，它为解决科学和工业各个领域中出现的许多重要统计挑战打开了大门。该项目旨在探索基础论证的演变，作为对现代数据科学问题和技术的回应。这项研究的结果有望扩大对统计和数据科学基础的理解。重点将是新思想在法医学、基因组学、差异隐私和空间统计中的应用。研究生，包括代表性不足群体的成员，将通过参与该项目的研究获得培训。在适当考虑到基准方法有望产生新的有用结果的统计推断领域后，该项目将在以下方向进行研究。(1)由于许多实际问题的基准分布的解析计算是不可行的，因此该项目将开发易于实现的算法来从广义基准分布中采样。这些算法将显著提高广义基准推理（GFI）的实际适用性，并为GFI理论研究的新技术发展提供起点。(2)项目将对GFI的基本问题进行深入研究，使其能够应用于流形。(3)该项目将为GFI应用于非参数问题奠定基础。非参数模型的灵活性将给GFI带来挑战，必须通过引入额外的约束来克服。(4)作为一项重要的应用，该项目将发展法医学证据强度的事后校准。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Fiducial inference is an alternative framework to making statistical inference that opens doors to solve many important statistical challenges arising in various fields of science and industry. This project aims at exploring the evolution of the fiducial argument as a response to modern data science questions and techniques. Results of this research are expected to expand the understanding of the foundations of statistics and data science. Emphasis will be given to applications of the new ideas in forensic science, genomics, differential privacy, and spatial statistics. Graduate students, including members of underrepresented groups, will receive training through research involvement in the project.Having given due consideration to areas of statistical inference where the fiducial approach is expected to lead to new and useful results, the project will conduct research in the following directions. (1) Since the analytic calculation of fiducial distributions for many practical questions is not feasible, the project will develop easy-to-implement algorithms to sample from generalized fiducial distributions. These algorithms will significantly improve the practical applicability of generalized fiducial inference (GFI) and serve as a starting point for developing new techniques for the theoretical study of GFI. (2) The project will undertake an in-depth investigation of fundamental issues of GFI so that it can be applied on manifolds. (3) The project will lay the groundwork to make GFI applicable to non-parametric problems. The flexibility of non-parametric models will provide a challenge to GFI that will have to be overcome by introducing additional constraints. (4) As an important application, the project will develop post-hoc calibration of the strength of evidence in forensic science.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.