# An efficient Monte Carlo method for valid prior-free possibilistic statistical inference

arXiv: https://arxiv.org/abs/2501.10585 · HTML: https://mlsanity.com/paper/2501.10585/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jan 2025.

## Built on by (most cited first, 1 of 1)

- [Beyond Prediction-Set Size: Quantifying Conformal Uncertainty through Credal Geometry](https://mlsanity.com/paper/2602.01667/) (2026)

## Abstract (arXiv)

Inferential models (IMs) offer prior-free, Bayesian-like posterior degrees of belief designed for statistical inference, which feature a frequentist-like calibration property that ensures reliability of said inferences. The catch is that IMs' degrees of belief are possibilistic rather than probabilistic and, since the familiar Monte Carlo methods approximate probabilistic quantities, there are significant computational challenges associated with putting this framework into practice. The present paper overcomes these challenges by developing a new Monte Carlo method designed specifically to approximate the IM's possibilistic output. The proposal is based on a characterization of the possibilistic IM's credal set, which identifies the "best probabilistic approximation" of the IM as a mixture distribution that can be readily approximated and sampled from. These samples can then be transformed into an approximation of the possibilistic IM. Numerical results are presented highlighting the proposed approximation's accuracy and computational efficiency.