Fisher's fiducial argument is widely viewed as a failed version of Neyman's theory of confidence limits. But Fisher's goal -- Bayesian-like probabilistic uncertainty quantification without priors -- was more ambitious than Neyman's, and it's not out of reach. I've recently shown that reliable, prior-free probabilistic uncertainty quantification must be grounded in the theory of imprecise probability, and I've put forward a possibility-theoretic solution that achieves it. This has been met with resistance, however, in part due to statisticians' singular focus on confidence limits. Indeed, if imprecision isn't needed to perform confidence-limit-related tasks, then what's the point? In this paper, for a class of practically useful models, I explain specifically why the fiducial argument gives valid confidence limits, i.e., it's the "best probabilistic approximation" of the possibilistic solution I recently advanced. This sheds new light on what the fiducial argument is doing and on what's lost in terms of reliability when imprecision is ignored and the fiducial argument is pushed for more than just confidence limits.

翻译：费雪的基准推断通常被视为内曼置信限理论的失败版本。但费雪的目标——无需先验即可实现类似贝叶斯概率的不确定性量化——比内曼的理论更具雄心，且并非遥不可及。我近期证明，可靠的无先验概率不确定性量化必须基于非精确概率理论，并提出了一个基于可能性理论的解决方案。然而，这一方案遭到部分抵制，主要因为统计学家过度聚焦于置信限。确实，如果无需非精确性即可完成置信限相关任务，那么引入非精确性意义何在？本文针对一类具有实际应用价值的模型，具体阐释了为何基准推断能给出有效的置信限——即它是我近期提出的可能论解决方案的“最佳概率近似”。这为理解基准推断的本质，以及忽视非精确性、将基准推断应用于置信限之外时损失的可靠性，提供了全新视角。