Collaborative Research: Emerging Variants of Generalized Fiducial Inference

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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.