Collaborative Research: Emerging Variants of Generalized Fiducial Inference

协作研究：广义基准推理的新兴变体

基本信息

批准号：
2210337
负责人：
Jan Hannig
金额：
$ 16万
依托单位：
University of North Carolina at Chapel Hill
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2022
资助国家：
美国
起止时间：
2022-09-01 至 2025-08-31
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2210337&HistoricalAwards=false
关键词：
Collaborative Research Emerging Variants Generalized

项目摘要

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.

基准推断是制定统计推断的替代框架，该框架为解决科学和工业领域引起的许多重要统计挑战打开了。该项目旨在探索基准论点的演变，以此作为对现代数据科学问题和技术的回答。这项研究的结果有望扩大对统计和数据科学基础的理解。将重点放在法医学，基因组学，差异隐私和空间统计数据中的新思想的应用。研究生，包括代表性不足的群体的成员，将通过研究参与进行培训。给予适当考虑统计推断领域的统计推断领域，预计基准方法将带来新的有用结果，该项目将在以下方向上进行研究。（1）由于许多实际问题的基准分布的分析计算是不可行的，因此该项目将开发易于实施算法，以从广义基准分布中进行采样。这些算法将显着提高广义基金推断（GFI）的实际适用性，并成为开发GFI理论研究新技术的起点。（2）该项目将对GFI的基本问题进行深入的调查，以便将其应用于流形。（3）该项目将奠定基础，使GFI适用于非参数问题。非参数模型的灵活性将为GFI提供挑战，必须通过引入其他约束来克服。（4）作为一项重要应用，该项目将在法医科学中对证据实力进行事后校准。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的智力优点和更广泛影响的评估标准来通过评估来获得支持的。