Motivated by parametric models for which the likelihood is analytically unavailable, numerically unstable, or prohibitively expensive to compute or optimize, we develop a prior- and likelihood-free framework for fully probabilistic (Bayesian-like) uncertainty quantification with finite-sample calibration guarantees. Our method, a type of inferential model, produces data-dependent degrees of belief about claims concerning the unknown parameter while controlling the frequency with which high belief is assigned to false claims, even in finite-sample settings. Our procedure is general in that it requires only the ability to simulate from the model. We first rank candidate parameter values according to how well data simulated from the model agree with the observed data, and then rescale these rankings in a way that yields the desired finite-sample calibration guarantees. The key idea is to employ a permutation-invariant function, such as a depth function, to rank parameter values. We show that such a choice yields closed-form calibration rescaling calculations, making the procedure computationally simple. We illustrate our method's broad appeal with four examples, including differential privacy and Ising models. An analysis of the spatial configuration of 2025 measles outbreaks in the U.S. showcases our method's practical advantages.

翻译：针对似然函数解析不可得、数值不稳定或计算/优化成本过高的参数模型，本文提出一种先验与似然无关的完全概率（类贝叶斯）不确定性量化框架，该框架具备有限样本校准保证。我们的方法作为推断模型的一种形式，能够生成关于未知参数命题的数据依赖型置信度，同时控制有限样本情境下将高置信度赋予错误命题的频率。本方法具有普适性，仅需具备从模型进行仿真的能力。我们首先根据模型仿真数据与观测数据的吻合程度对候选参数值进行排序，随后通过尺度变换将这些排序值转化为具有有限样本校准保证的置信度量。核心思想是采用置换不变函数（如深度函数）对参数值进行排序。我们证明此类选择能够导出闭式校准尺度变换计算，使流程具有计算简洁性。通过差分隐私和伊辛模型等四个示例，我们展示了本方法的广泛适用性。对美国2025例麻疹疫情空间构型的分析，彰显了本方法的实践优势。