Collaborative Research: Generalized Fiducial Inference in Complex Systems: Causal Inference, Networks, and Normalizing Flows

Accurate statistical inference is essential for making reliable decisions in various fields, such as forensic science, medicine, economics, and machine learning. This project develops and advances generalized fiducial inference (GFI), an innovative statistical method that quantifies uncertainty without requiring subjective assumptions. By addressing complex real-world problems, such as evaluating evidence in criminal cases, understanding causal relationships in economics and health, and improving reliability in machine learning, the project will significantly enhance decision-making processes. Additionally, the project provides valuable research training opportunities for graduate students in science, technology, engineering, and mathematics (STEM), thereby contributing directly to national goals of promoting scientific advancement, health, prosperity, and welfare. This collaborative research aims to advance generalized fiducial inference (GFI), building upon Fisher’s original fiducial argument and recent developments in modern statistics. The primary objectives include extending GFI methods to causal inference models, particularly instrumental variable models, and redefining GFI through normalizing flows to manage computational complexity in non-analytic scenarios. The project will also apply these methodological innovations to pressing real-world problems in forensic science, specifically addressing the accurate calibration of likelihood ratios from machine learning models, as well as, resources permitting, investigations into uncertainty quantification for social network learning and sports analytics. 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.