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

TL;DR

This paper introduces a novel Monte Carlo method tailored for possibilistic inferential models, enabling efficient approximation of their belief measures while maintaining calibration and reliability.

Contribution

It develops a new Monte Carlo approach that approximates possibilistic inferential models using a mixture distribution, addressing computational challenges.

Findings

The method accurately approximates IM's credal set.

It demonstrates improved computational efficiency.

Numerical results confirm reliable and fast inference.

Abstract

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.