# Extended Fiducial Inference: Toward an Automated Process of Statistical Inference

arXiv: https://arxiv.org/abs/2407.21622 · HTML: https://mlsanity.com/paper/2407.21622/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 96 references that are in the map.
- First posted on arXiv 31 Jul 2024.

## Builds on (most cited first, 4 of 4)

- [An Overview of Deep Semi-Supervised Learning](https://mlsanity.com/paper/2006.05278/) (2020)
- [Generalized Fiducial Inference on Differentiable Manifolds](https://mlsanity.com/paper/2209.15473/) (2022)
- [Optimal tests of the composite null hypothesis arising in mediation analysis](https://mlsanity.com/paper/2107.07575/) (2021)
- [A Geometric Perspective on Bayesian and Generalized Fiducial Inference](https://mlsanity.com/paper/2210.05462/) (2022)

## Built on by (most cited first, 2 of 2)

- [Uncertainty Quantification for Physics-Informed Neural Networks with Extended Fiducial Inference](https://mlsanity.com/paper/2505.19136/) (2025)
- [Extended Fiducial Inference for Individual Treatment Effects via Deep Neural Networks](https://mlsanity.com/paper/2505.01995/) (2025)

## Abstract (arXiv)

While fiducial inference was widely considered a big blunder by R.A. Fisher, the goal he initially set --`inferring the uncertainty of model parameters on the basis of observations' -- has been continually pursued by many statisticians. To this end, we develop a new statistical inference method called extended Fiducial inference (EFI). The new method achieves the goal of fiducial inference by leveraging advanced statistical computing techniques while remaining scalable for big data. EFI involves jointly imputing random errors realized in observations using stochastic gradient Markov chain Monte Carlo and estimating the inverse function using a sparse deep neural network (DNN). The consistency of the sparse DNN estimator ensures that the uncertainty embedded in observations is properly propagated to model parameters through the estimated inverse function, thereby validating downstream statistical inference. Compared to frequentist and Bayesian methods, EFI offers significant advantages in parameter estimation and hypothesis testing. Specifically, EFI provides higher fidelity in parameter estimation, especially when outliers are present in the observations; and eliminates the need for theoretical reference distributions in hypothesis testing, thereby automating the statistical inference process. EFI also provides an innovative framework for semi-supervised learning.