An Efficient Monte Carlo Method for Valid Prior-Free Possibilistic Statistical Inference

• 成果类型: Article; Early Access
• 署名作者: Martin, Ryan
• 署名单位: North Carolina State University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459; 1537-274X
• DOI: 10.1080/01621459.2026.2671450
• 发表日期: 2026-06-19
• 关键词: confidence distribution; Credal set; Gaussian possibility; Inferential model; sampling algorithm; FREE PROBABILISTIC INFERENCE; belief functions; confidence; models

摘要

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 article 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. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.