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：费歇尔的基准论证普遍被视为内曼置信限理论的一个失败版本。但费歇尔的目标——无需先验的贝叶斯式概率不确定性量化——比内曼更为宏大，且并非遥不可及。我近期已证明，可靠的、无先验的概率不确定性量化必须基于不精确概率理论，并提出了一个实现该目标的可能性理论解决方案。然而,这一方案遭遇了阻力,部分源于统计学家对置信限的单一关注。诚然,如果执行置信限相关任务无需不精确性,那么其意义何在？本文针对一类实用模型,具体阐释了为何基准论证能给出有效的置信限——即它是对我近期提出的可能性解法的"最优概率近似"。这为理解基准论证的本质作用,以及因忽略不精确性、强行将基准论证用于置信限之外场景所牺牲的可靠性提供了全新视角。