The inferential model (IM) framework offers alternatives to the familiar probabilistic (e.g., Bayesian and fiducial) uncertainty quantification in statistical inference. Allowing this uncertainty quantification to be imprecise makes it possible to achieve exact validity and reliability. But is imprecision and exact validity compatible with attainment of the classical notions of statistical efficiency? The present paper offers an affirmative answer to this question via a new possibilistic Bernstein--von Mises theorem that parallels a fundamental result in Bayesian inference. Among other things, our result demonstrates that the IM solution is asymptotically efficient in the sense that its asymptotic credal set is the smallest that contains the Gaussian distribution whose variance agrees with the Cramer--Rao lower bound.

翻译：推断模型（IM）框架为统计推断中熟悉的概率性（例如，贝叶斯和信仰）不确定性量化提供了替代方案。允许这种不确定性量化不精确，使得实现精确有效性和可靠性成为可能。但不精确性和精确有效性是否与古典统计效率概念的达成相容？本文通过一个新的可能性Bernstein--von Mises定理，对此问题给出了肯定回答，该定理与贝叶斯推断中的基本结果相平行。尤其地，我们的结果表明，IM解在渐近意义上是有效的，其渐近信度集是包含方差与Cramer--Rao下界一致的高斯分布的最小集合。