# Model-free generalized fiducial inference

arXiv: https://arxiv.org/abs/2307.12472 · HTML: https://mlsanity.com/paper/2307.12472/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 62 references that are in the map.
- First posted on arXiv 24 Jul 2023.

## Builds on (most cited first, 15 of 15)

- [Conformal Risk Control](https://mlsanity.com/paper/2208.02814/) (2022)
- [Distribution-Free, Risk-Controlling Prediction Sets](https://mlsanity.com/paper/2101.02703/) (2021)
- [Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Control](https://mlsanity.com/paper/2110.01052/) (2021)
- [Game-theoretic statistics and safe anytime-valid inference](https://mlsanity.com/paper/2210.01948/) (2022)
- [Safe Testing](https://mlsanity.com/paper/1906.07801/) (2019)
- [Universal Inference](https://mlsanity.com/paper/1912.11436/) (2019)
- [Beyond Neyman-Pearson: e-values enable hypothesis testing with a data-driven alpha](https://mlsanity.com/paper/2205.00901/) (2022)
- [Decision under Uncertainty](https://mlsanity.com/paper/1304.1527/) (2013)
- [Validity, consonant plausibility measures, and conformal prediction](https://mlsanity.com/paper/2001.09225/) (2020)
- [False confidence, non-additive beliefs, and valid statistical inference](https://mlsanity.com/paper/1607.05051/) (2016)
- [An exposition of the false confidence theorem](https://mlsanity.com/paper/1807.06217/) (2018)
- [Discussion of "A Gibbs sampler for a class of random convex polytopes"](https://mlsanity.com/paper/2104.02717/) (2021)
- [Direct and approximately valid probabilistic inference on a class of statistical functionals](https://mlsanity.com/paper/2112.10232/) (2021)
- [Robust Universal Inference For Misspecified Models](https://mlsanity.com/paper/2307.04034/) (2023)
- [Valid Inference for Machine Learning Model Parameters](https://mlsanity.com/paper/2302.10840/) (2023)

## Abstract (arXiv)

Conformal prediction (CP) was developed to provide finite-sample probabilistic prediction guarantees. While CP algorithms are a relatively general-purpose approach to uncertainty quantification, with finite-sample guarantees, they lack versatility. Namely, the CP approach does not em prescribe how to quantify the degree to which a data set provides evidence in support of (or against) an arbitrary event from a general class of events. In this paper, tools are offered from imprecise probability theory to build a formal connection between CP and generalized fiducial (GF) inference. These new insights establish a more general inferential lens from which CP can be understood, and demonstrate the pragmatism of fiducial ideas. The formal connection establishes a context in which epistemically-derived GF probability matches aleatoric/frequentist probability. Beyond this fact, it is illustrated how tools from imprecise probability theory, namely lower and upper probability functions, can be applied in the context of the imprecise GF distribution to provide posterior-like, prescriptive inference that is not possible within the CP framework alone. In addition to the primary CP generalization that is contributed, fundamental connections are synthesized between this new model-free GF and three other areas of contemporary research: nonparametric predictive inference (NPI), conformal predictive systems/distributions, and inferential models (IMs).